Unit 1, Activity 1, Graphically Speaking
Advanced
Mathematics
Functions and
Statistics
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 1
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Unit 1, Activity 1, Graphically Speaking
1.
a) Domain: _______________ b) Range: ________________ c) Max: ______________
d) Inc: __________________
e) Dec: __________________ f) Constant: ___________
g) f(-3) = ________________
h) f(x) = 0 ________________ i) f(x) > 0 ____________
2.
a) Domain: _______________ b) Range: ________________ c) Min: ______________
d) Inc: __________________
e) Dec: __________________ f) Constant: ___________
g) f(0) = _________________ h) f(x) = 3 _________________ i) f(x) < 0 ____________
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 1
Unit 1, Activity 1, Graphically Speaking
3.
a) Domain: _______________ b) Range: ________________ c) Min: ______________
d) Inc: __________________
e) Dec: __________________ f) Constant: ___________
g) f(1) = ________________
h) f(x) = -1_________ ______ i) f(x) < 0 ____________
4.
a) Domain: _______________ b) Range: ________________ c) Max: ______________
d) Inc: __________________
e) Dec: __________________ f) Constant: ___________
g) f(-1) = ________________
h) f(x) = -2 _______________ i) f(x) > 0 ____________
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 2
Unit 1, Activity 1, Graphically Speaking with Answers
1.
a) Domain: __[-4, 5]
b) Range: ____[-3, 4]
____ c) Max: _____4 _______
d) Inc: _____(-4, 1)________
e) Dec: ___(1, 2)___________ f) Constant: __(2, 5)_____
g) f(-3) = _____2__________
h) f(x) = 0 _x = -4 ; x = 1.5__ i) f(x) > 0 __(-4, 1.5)____
2.
a) Domain: ____[-3, 6] _____ b) Range: ___[-1, 3] _______ c) Min: _____-1 ______
d) Inc: ______(-3,6) ______
e) Dec: _(-3, -1)  (1, 3)_____ f) Constant: __(-1, 1) ___
g) f(0) = ______1 ________
h) f(x) = 3 __x = -3 ; x = 6___
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
i) f(x) < 0 __ (2, 5) ____
Page 3
Unit 1, Activity 1, Graphically Speaking with Answers
3.
a) Domain: ____(-5, ) _____ b) Range: _
____
e) Dec: _____(-5, 0) ______ f) Constant: ___(4, )___
_______
h) f(x) = -1__x = -2 ; x  4___ i) f(x) < 0 ___(-4, ) ___
d) Inc: _______(0, 4)
g) f(1) = ____-3
_[-4, 3)______ c) Min: _____-4 ______
4.
a) Domain: ____(-, ) ____ b) Range: ____(-2, )_______ c) Max: ___none_______
d) Inc: __(-2, -1)  (2, ) __
e) Dec: _____(-1, 2)_________ f) Constant: __(-, -2)___
g) f(-1) = ___ 2___________
h) f(x) = -2 _____x = 2_______ i) f(x) > 0 (-, 0)  (4,)
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 4
Unit 1, Activity 2, Family of Functions
Function
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 5
Unit 1, Activity 2, Family of Functions
Function
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 6
Unit 1, Activity 2, Family of Functions with Answers
Function
Constant
Graph
Domain
Range
Extrema
Increasing/Dec.
(-, )
[k]
None
None
(-, )
(-, )
None
Inc. (-, )
(-, )
[0, )
(0, 0)
(-, )
(-, )
None
(-, )
[0, )
[0, )
None
Inc.[0, )
f(x) = k
Linear
f(x) = x
Quadratic
Inc. (0, )
Dec. (-, 0)
f(x) = x2
Cubic
f(x) =
x3
Square Root
f(x) =
x
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 7
Unit 1, Activity 2, Family of Functions with Answers
Function
Cube Root
f(x) =
3
Domain
Range
Extrema
Increasing/Dec.
(-, )
(-, )
None
Inc. (-, )
(-, )
(0, )
None
Inc. (-, )
(0, )
(-, )
None
Inc. (0, )
(-, )
[0, )
Min (0, 0)
(-, )
Integers
None
x
Exponential
f(x) =
Graph
ex
Logarithmic
f(x) = ln x
Absolute
Value
Inc. (0, )
Dec. (-, 0)
f(x) = x
Greatest
Integer
None
f(x) = [ x ]
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 8
Unit 1, Activity 3, Translations, Dilations, and Reflections
Graph
Type of
Function
Description of
Change
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Equation
Page 9
Unit 1, Activity 3, Translations, Dilations, and Reflections
Equation
f(x) =
1
+3
x2
f(x) =
 4x - 1
Description of Change
Graph – Parent
Graph - Final
f(x) = ½ (x – 1)2 - 2
f(x) = -3 ln (2x)
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 10
Unit 1, Activity 3, Translations, Dilations, and Reflections with Answers
Graph
Type of
Function
Description of
Change
Equation
Up 2
Linear
Vertical stretch of
factor 3
f(x) = -3x + 2
Reflect over x-axis
Right 1
Cubic
Vertical stretch of
factor 2
f(x) = -2(x - 1)3
Reflect over x-axis
Cube root
Vertical
compression of
factor 2
f(x) =
1
2
3
1
x
2
Horizontal stretch
of factor 2
Right 1
Exponential
Down 2
f(x) = e1-x - 2
Reflect over y-axis
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 11
Unit 1, Activity 3, Translations, Dilations, and Reflections with Answers
Equation
f(x) =
f(x) =
1
+3
x2
 4x - 1
Descripti
on of
Change
Graph – Parent
Graph - Final
Left 2
Up 3
Reflect
over yaxis
Horizontal
compressi
on of
factor 4
Down 1
f(x) = ½ (x – 1)2 - 2
Vertical
compressi
on of
factor 2
Right 1
Down 2
f(x) = -3 ln ( ½ x)
Reflect
over xaxis
Vertical
stretch of
factor 3
Horizontal
stretch of
factor 2
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 12
Unit 1, Activity 4, In Pieces
Tax Model #1
Citizens earning $5000 and up to $80,000 will pay a personal income tax of 10%. Citizens
earning $80,000 and up to $200,000 will pay 20%. Citizens making $200,000 and above will
pay an income tax of 25%.
1. Write a function to model this tax structure.
2. Draw the graph of the tax model.
3. Is this particular tax structure fair? Why or why not?
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 13
Unit 1, Activity 4, In Pieces with Answers
Tax Model #1
Citizens earning $5000 and up to 80,000 will pay a personal income tax of 10%. Citizens
earning $80,000 and up to $200,000 will pay 20%. Citizens making $200,000 and above will
pay an income tax of 25%.
1. Write a function to model this tax structure.
f(x) =

.15x ; 5,000  x < 80,000
.20x ; 80,000  x < 200,000
.25x ; 200,000  x
2. Draw the graph of the tax model.
3. Is this particular tax structure fair? Why or why not?
Answers will vary, but students should identify this tax structure as being progressive since
the tax increases as the income increases.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 14
Unit 1, Activity 7, Inverse Functions
Split-Page Notetaking
Topic: Inverse Functions
Verbal Representation
Date: ___________
Example #1
amount you pay for gas
number of gallons purchased
Function
The total cost of the gas is dependent on the number of
gallons purchased.
Ordered Pairs
(number of gallons, total cost)
Inverse Function
The number of gallons that can be purchased depends on
the amount of money you have.
Inverse Ordered Pairs
(total cost, number of gallons)
Example #2
Number of hours worked
amount of paycheck
Function
The amount of your paycheck is dependent on the
number of hours you worked.
Ordered Pairs
(number of hours, amount of paycheck)
Inverse Function
The number of hours you need to work depends on the
amount of money you need to earn.
Inverse Ordered Pairs
(amount of paycheck, number of hours)
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 15
Unit 2, Activity 1, Solving Right Triangles
Solve each triangle.
1.
A
4m
C
2.
10 m
A
A
____________ a ___________
B
____________ b ___________
C
____________ c ___________
A
____________ a ___________
B
____________ b ___________
C
____________ c ___________
A
____________ a ___________
B
____________ b ___________
C
____________ c ___________
B
9 ft
C
15 ft
B
3.
A
45
14 km
C
B
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 16
Unit 2, Activity 1, Solving Right Triangles
B
4.
38
A
5.
11 m
A
____________ a ___________
B
____________ b ___________
C
____________ c ___________
A
____________ a ___________
B
____________ b ___________
C
____________ c ___________
C
C
B
24 yd
60
A
6.
A
35 m
A ____________ a ___________
B
____________ b ___________
C
____________ c ___________
53
B
C
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 17
Unit 2, Activity 1, Solving Right Triangles with Answers
Solve each triangle.
1.
A  _681155__ a = __10 m____
A
B  _21485___ b = ___4 m____
4m
C = ____90____ c = 2 29 m
C
10 m
102 + 42 =c2
c2 = 116
2.
A
B
tan A = 10/4
A = tan -1 (10/4)
A  68.2
9 ft
A  _53 748__
C
a = _12 ft_____
B  _365212__ b = __ 9 ft_____
15 ft
C = ___90______ c = __15 ft____
B
a2 = 152 - 92 OR 3 - 4 - 5
a2 = 144
9-12-15
3.
cos A = 9/15
A = cos -1 (9/15)
A  53.1
A = ____45_____ a = 7 2 km
A
45
B = ____45_____ b = 7 2 km
14 km
C = ____90_____ c = __14 km___
C
a=
B
14
2
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 18
Unit 2, Activity 1, Solving Right Triangles with Answers
B
A = ___38_____ a  __8.6 m____
4.
B = ____52_____ b = __11 m____
C = ____90_____ c  __14.0 m___
38
A
11 m
C
tan 38 = a/11
a = 11 tan 38
5.
cos 38 = 11/c
c = 11/cos 38
C
A = ___60______ a = 12 3 yd
B
B = ___30______ b = __12_yd___
24 yd
60
C = __90_______ c = __24 yd ___
A
short leg  2 = 24
6.
long leg = 12 
3
A = ___27_____ a  __21.1 m___
A
B = ___53______ b  __28.0 m___
C = ___90______ c = ___35 m___
35 m
53
B
cos 53 = a/35
a = 35 cos 53
C
sin 53 = b/35
b = 35 sin 53
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 19
Unit 2, Activity 2, Applications of Right Triangles
Problem
1. Height of an object
Solution
Check
2. Angle of elevation or depression
3. Vector components
(hor. & vert. OR dir. & mag.)
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 20
Unit 2, Activity 3, Discovering the Law of Sines
ABC is an oblique triangle.
C
A
B
1. Draw an altitude from vertex C.
2. Label the altitude x.
3. Use right triangle trigonometry to complete the ratios below.
sin A =
sin B =
4. Solve each of the above equations for x.
5. Set the above equations equal to each other to form a new equation. Why is this
possible?
6. Regroup the variables so that each capital letter is on the same side of the equal sign as its
lower case counterpart.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 21
Unit 2, Activity 3, Discovering the Law of Sines
ABC is an oblique triangle.
C
A
B
7. Draw an altitude from vertex B.
8. Label the altitude x.
9. Use right triangle trigonometry to complete the ratios below.
sin A =
sin C =
10. Solve each of the above equations for x.
11. Set the above equations equal to each other to form a new equation. Why is this
possible?
12. Regroup the variables so that each capital letter is on the same side of the equal sign as
its lower case counterpart.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 22
Unit 2, Activity 3, Discovering the Law of Sines
ABC is an oblique triangle.
C
A
B
13. Draw an altitude from vertex A.
14.
Label the altitude x.
15. Use right triangle trigonometry to complete the ratios below.
sin B =
sin C =
16. Solve each of the above equations for x.
17. Set the above equations equal to each other to form a new equation. Why is this
possible?
18. Regroup the variables so that each capital letter is on the same side of the equal sign as
its lower case counterpart.
19. Use the results from 1-18 to write the Law of Sines.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 23
Unit 2, Activity 3, Discovering the Law of Sines with Answers
ABC is an oblique triangle.
C
x
A
B
1. Draw an altitude from vertex C.
2. Label the altitude x.
3. Use right triangle trigonometry to complete the ratios below.
sin A =
x
b
sin B =
x
a
4. Solve each of the above equations for x.
x = b sin A
x = a sin B
5. Set the above equations equal to each other to form a new equation. Why is this
possible?
b sin A = a sin B
The transitive property makes this possible.
6. Regroup the variables so that each capital letter is on the same side of the equal sign as its
lower case counterpart.
sin A
sin B

a
b
OR
a
b

sin A
sin B
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 24
Unit 2, Activity 3, Discovering the Law of Sines with Answers
ABC is an oblique triangle.
C
x
A
B
7. Draw an altitude from vertex B.
8. Label the altitude x.
9. Use right triangle trigonometry to complete the ratios below.
sin A =
x
c
sin C =
x
a
10. Solve each of the above equations for x.
x = c sin A
x = a sin C
11. Set the above equations equal to each other to form a new equation. Why is this
possible?
c sin A = a sin C
The transitive property makes this possible.
12. Regroup the variables so that each capital letter is on the same side of the equal sign as
its lower case counterpart.
sin A
sin C

a
c
OR
a
c

sin A
sin C
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 25
Unit 2, Activity 3, Discovering the Law of Sines with Answers
ABC is an oblique triangle.
C
x
A
B
13. Draw an altitude from vertex A.
14. Label the altitude x.
15. Use right triangle trigonometry to complete the ratios below.
sin B =
x
c
sin C =
x
b
16. Solve each of the above equations for x.
x = c sin B
x = b sin C
17. Set the above equations equal to each other to form a new equation. Why is this
possible?
c sin B = b sin C
The transitive property makes this possible.
18. Regroup the variables so that each capital letter is on the same side of the equal sign
as its lower case counterpart.
sin B
sin C

b
c
OR
b
c

sin B
sin C
19. Use the results from 1-18 to write the Law of Sines.
sin A
sin B
sin C


a
b
c
OR
a
b
c


sin A
sin B
sin C
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 26
Unit 2, Activity 3, Law of Sines: Split-Page Notetaking
Split-Page Notetaking
Topic: Law of Sines
Date: _____________________
AAS
Example
B = 180- 88- 43 = 49
Unique triangle
A
88
B
43
b
11

sin 49 sin 88
b  8.3 m
c
11

sin 43 sin 88
c  7.5 m
C
11 m
*To make the calculations easier, put the unknown
value in the numerator.
SSA – Obtuse Angle
sin A sin 106

17
34
Unique triangle
B
106
A
C  180 - 28.7 - 106  45.3  451624
17 km
C
34 km
A  28.7  284336
c
34

sin 45.3 sin 106
c  25.1 km
*Since a triangle can have only one obtuse angle, a
unique triangle exists.
SSA – Obtuse Angle
No triangle
A
25 m
B
28 m
The Law of Sines is not needed; however, it will
reveal no triangle. A triangle can have only one
obtuse angle. In this case, it is C. Thus, c must be
the longest side. Since b > c, no triangle with these
measurements exists.
117
C
sin A sin 117

28
25
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
A  86.3  861837
A + C > 180
Page 27
Unit 2, Activity 4, Discovering the Law of Cosines
C
b
a
A
c
B
1. Draw an altitude from vertex C and label it h.
2. The altitude divides c into two different pieces. Label one piece x. How can you label the
other piece in terms of x and c?
3. Using the Pythagorean Theorem, write two different equations for each right triangle.
4. Solve each equation for h2.
5. Set the two equations equal to each other to form a new equation. Why can this be done?
6. Which variable in the equation is not a side of ABC?
7. Solve the equation for b2 and expand (c – x)2. What happens to the x2?
8. Since x is not a side of ABC, it needs to be eliminated. What do you suggest?
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 28
Unit 2, Activity 4, Discovering the Law of Cosines
9. Write an equation relating x and cos B and then solve for x.
10. Replace x in the equation from #7 with its equivalent expression found above.
11. This part of the Law of Cosines finds the length of side b. Based on the work for #1-10,
write equations to find the lengths of sides a and c.
12. Rewrite each of the three equations to find angles A, B, and C.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 29
Unit 2, Activity 4, Discovering the Law of Cosines with Answers
C
b
h
A
c-x
a
x
B
1. Draw an altitude from vertex C and label it h.
2. The altitude divides c into two different pieces. Label one piece x. How can you label the
other piece in terms of x and c?
3. Using the Pythagorean Theorem, write two different equations for each right triangle.
(c – x)2 + h2 = b2
x2 + h2 = a2
4. Solve each equation for h2.
h2 = b2 – (c – x)2
h2 = a2 – x2
5. Set the two equations equal to each other to form a new equation. Why can this be done?
b2 – (c – x)2 = a2 – x2
The transitive property makes this possible.
6. Which variable in the equation is not a side of ABC?
x
7. Solve the equation for b2 and expand (c – x)2. What happens to the x2?
b2 = a2 – x2 + (c – x)2
b2 = a2 + c2 – 2cx
The x2s cancel each other out.
8. Since x is not a side of ABC, it needs to be eliminated. What do you suggest?
Answers will vary
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 30
Unit 2, Activity 4, Discovering the Law of Cosines with Answers
9. Write an equation relating x and cos B and then solve for x.
cos B =
x
a
x = a cos B
10. Replace x in the equation from #7 with its equivalent expression found above.
b2 = a2 + c2 – 2c(a cos B)
b2 = a2 + c2 – 2ac cos B
11. This part of the Law of Cosines finds the length of side b. Based on the work for #1-10,
write equations to find the lengths of sides a and c.
It is not necessary to rework the steps #1-10. Students should be able to use patterns to
generate the other two equations.
a2 = b2 + c2 – 2bc cos A
c2 = a2 + b2 – 2ab cos C
12. Rewrite each of the three equations to find angles A, B, and C.
2bc cos A = b2 + c2 – a2
cos A =
2ac cos B = a2 + c2 – b2
b2  c2  a2
2bc
cos B =
 b2  c2  a2 

A = cos -1 
2bc


a2  c2  b2
2ac
 a2  c2  b2 

B = cos -1 
2ac


2ab cos C = a2 + b2 – c2
cos C =
a2  b2  c2
2ab
 a2  b2  c2 

C = cos -1 
2ab


Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 31
Unit 2, Activity 5, Applications of Oblique Triangles
1. To find the width of a lake, a surveyor stands 136 m from one end of the lake and 162 m
from the other end at an angle of 78. What is the width of the lake?
2. A surveying crew needs to find the distance between two points, A and B, but a boulder
between the two points makes a direct measurement impossible. Thus, the crew moves to a
point C that is at an angle of 110 to points A and B. The distance between C and B is 422 ft
and the angle from A is 30. What is the distance between points A and B?
3. Two coast guard stations are 150 miles apart. A ship at sea sends out a distress call that is
received by both stations. The angle from one station to the ship is 55. The angle from the
other station to the ship is 36. How far is the ship from the closest station?
4. A Major League baseball diamond is a square with sides measuring 90 ft each. The pitching
rubber is 60.5 ft from home plate on a line joining home plate and second base. How far is it
from the pitching rubber to first base?
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 32
Unit 2, Activity 5, Applications of Oblique Triangles
5. The area of an oblique triangle can be found using the formula A = ½ ab sin C. To use
this formula, two sides and the included angle must be known. Find the appropriate side in
order to determine the area of the triangle below.
17 in.
53
30
6. Heron’s formula, A = ss  a s  bs  c  , is used to find the area of an oblique triangle
when all three sides are known. The variable s represents the semi-perimeter (half the
perimeter). Find the third side and then use Heron’s formula to find the area of the triangle.
22 m
43
16 m
7. A boat is traveling 8 knots at a bearing of 100. After two hours, the boats turns and travels
at a bearing of 55 for three hours at 10 knots. Find the magnitude and the direction of the
displacement vector.
8. A plane is flying due East at 300 mph. A tailwind is blowing 25 west of North at 15 mph.
What is the actual direction and velocity of the plane?
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 33
Unit 2, Activity 5, Applications of Oblique Triangles with Answers
1. To find the width of a lake, a surveyor stands 136 m from one end of the lake and 162 m
from the other of the lake at an angle of 78. What is the width of the lake?
a2 = 1622 + 1362 – 2(162)(236) cos 78
a  188.6 m
78
162 m
136 m
a
2. A surveying crew needs to find the distance between two points, A and B, but a boulder
between the two points makes a direct measurement impossible. Thus, the crew moves to a
point C that is at an angle of 110 to points A and B. The distance between C and B is 422 ft
and the angle from A is 30. What is the distance between points A and B?
c
422

sin 110 sin 30
C
110
c  793.1 ft
422 ft
30
A
c
B
3. Two coast guard stations are 150 miles apart. A ship at sea sends out a distress call that is
received by both stations. The angle from one station to the ship is 55. The angle from the
other station to the ship is 36. How far is the ship from the closest station?
a
150

sin 36 sin 89
ship
a
55
36
a  88.2 mi
150 mi
4. A Major League baseball diamond is a square with sides measuring 90 ft each. The pitching
rubber is 60.5 ft from home plate on a line joining home plate and second base. How far is it
from the pitching rubber to first base?
a2 = 60.52 + 902 – 2(60.5)(90) cos 45
a  63.7 ft
a
60.5 ft
45
90 ft
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 34
Unit 2, Activity 5, Applications of Oblique Triangles with Answers
5. The area of an oblique triangle can be found using the formula A = ½ ab sin C. To use
this formula, two sides and the included angle must be known. Find the appropriate side in
order to determine the area of the triangle below.
a
17

17 in.
A  ½ (17)(21.1)sin 30
sin 97 sin 53
A  89.7 in2
53
30
a  21.1 in.
a
6. Heron’s formula, A = ss  a s  bs  c  , is used to find the area of an oblique triangle
when all three sides are known. The variable s represents the semi-perimeter (half the
perimeter). Find the third side and then use Heron’s formula to find the area of the triangle.
22 m
B
43
sin C sin 43

22
16
A
C  180 - 69.7  110.3
b
16

sin 26.7 sin 43
16 m
C
b  10.5 m
Area  24.2524.25  1624.25  2224.25  10.5
Area  78.7 m2
7. A boat is traveling 8 knots at a bearing of 100. After two hours, the boats turns and travels
at a bearing of 55 for three hours at 10 knots. Find the magnitude and the direction of the
displacement vector.
Extended angle = 45
N
B = 180- 45 = 135
N
b
A
C
b2 = 162+302-2(16)(30)cos135
b  42.8 n. mi
100
16 n. mi
55
B
30 n. mi
sin BAC sin 135

BAC  29.7
30
42.8
Direction: bearing of 100- 29.7  70.3
8. A plane is flying due East at 300 mph. A tailwind is blowing 25 west of North at 15 mph.
What is the actual direction and velocity of the plane?
Extended angle = 90
N
C
N
B = 180- 90- 25 = 65
b
b2 = 152 + 3002 – 2(15)(300)cos 65
15mph 25
b  294.0 mph
sin BAC sin 65

A
300 mph
B
BAC2.7
15
294
Direction: bearing of 90-2.7 87.3 (east of North)
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 35
Unit 3, Activity 1, Know Thyself
Rate your understanding of each mathematical term with a “+” if you understand the term well, a
“” if you have a limited understanding of the term, or a “-” if you have no understanding of the
term at all. You should continually revise your entries as you progress through unit 2. Since this
is a self-awareness activity, you will not share your entries with the rest of the class. So, be
honest with yourself!
Term(s)
+

-
Definition
Example
Power
Function
Polynomial
Function
Domain
Range
Zero
Zero
Multiplicity
End Behavior
Extrema
Increasing
Intervals
Decreasing
Intervals
Symmetry
Even Function
Odd Function
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 36
Unit 3, Activity 2, Power Functions – Positive Integer Exponents
Fill in the following word grid for y  x p . Start the first row with p = 1. Fill in the first column
with important function properties and components.
f(x) = xp
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 37
Unit 3, Activity 2, Power Functions – Positive Integer Exponents with Answers
Fill in the following word grid for y  x p . Start with p = 1.
f(x) = xp
f(x) = x
f(x) = x2
f(x) = x3
f(x) = x4
Domain
(-, )
(-, )
(-, )
(-, )
Range
(-, )
[0, )
(-, )
[0, )
Behavior
as x  
y
y
y
y
Behavior
as
x  
y  -
y
y  -
y
Extrema
None
(0, 0)
None
(0, 0)
Symmetry
Origin
y-axis
Origin
y-axis
Graph
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 38
Unit 3, Activity 4, Polynomial Functions & Their Graphs
Use technology to complete the chart.
Function
f(x) = (x+1)2
f(x) = -x(x-2)(x+3)
f(x) = -x2(x-5)2
f(x) = x3(x2-4)
Sketch
Parent
Zeros
Root
Characteristics
End Behavior
x 
End Behavior
x -
Relative and
Absolute
Extrema
Increasing
Intervals
Decreasing
Intervals
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 39
Unit 3, Activity 4, Polynomial Functions & Their Graphs with Answers
Use technology to complete the chart.
f(x) = (x+1)2
f(x) = -x(x-2)(x+3)
f(x) = -x2(x-5)2
f(x) = x3(x2-4)
Parent
f(x) = x2
f(x) = x3
f(x) = x4
f(x) = x5
Zeros
-1
0, 2, -3
0, 5
0, -2, 2
Double root
and tangent to
x-axis at x = -1
Crosses at 0
Crosses at 2
Crosses at -3
Double root
and tangent to
x-axis at x = 0
and at x = 5
Crosses at 0
Crosses at -2
Crosses at 2
End Behavior
x 
y 
y -
y -
y 
End Behavior
x -
y 
y 
y -
y -
Relative and
Absolute
Extrema
Rel. Min.
Ab. Min.
(-1, 0)
(-1.786, -2.209)
Rel. Max.
(1.120, 4.061)
Ab. Max.
(0, 0) & (5, 0)
Rel. Min.
(2.5, -39.0625)
Increasing
Intervals
(-1, )
(-2.209, 1.120)
(-,0)  (2.5,5)
(-, -1.549) 
(1.549, )
Decreasing
Intervals
(-, -1)
(-, -2.209) 
(1.120, )
(0, 2.5)  (5, )
(-1.549, 1.549)
Function
Sketch
Root
Characteristics
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Rel. Max.
(-1.549, 5.949)
Rel. Min.
(1.549, -5.949)
Page 40
Unit 3, Activity 5, Polynomial Functions & Their Linear Factors
1. Graph the lines y = x + 2 and y = x – 4 on the coordinate axes below.
y
x
2. Sketch the quadratic function formed by multiplying the linear expressions in #1 on the same
coordinate axes.
3. What do you notice about the x- and y-intercepts of the parabola?
4. Use the graphs above to complete the sign chart below.
Quadratic function: f(x) = (x + 2)(x – 4)
Linear factor: x - 4
Linear factor: x + 2
-2
4
5. Use the sign chart above to answer the questions below.
a) Is the y value of the quadratic function positive or negative when x = 0? ______________
b) Is the y value of the quadratic function positive or negative when x = -7? _____________
c) For what values of x is (x + 2)(x – 4) > 0? ______________
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 41
Unit 3, Activity 5, Polynomial Functions & Their Linear Factors
6. Graph the lines y = x + 1, y = 2 – x, and y = x – 5 on the coordinate axes below
y
x
7. Sketch the cubic function formed by multiplying the linear expressions in #1 on the same
coordinate axes.
8. What do you notice about the x- and y-intercepts of the cubic function?
9. Use the graphs above to complete the sign chart below.
Cubic function: f(x) = (x + 1)(2 – x)(x - 5)
Linear factor: x - 5
Linear factor: 2 - x
Linear factor: x + 1
-1
2
5
10. Use the sign chart above to answer the questions below.
a) Is the y value of the quadratic function positive or negative when x = 13? ______________
b) Is the y value of the quadratic function positive or negative when x = -2? _____________
c) For what values of x is (x + 1)(2 – x)(x + 5)  0? ______________
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 42
Unit 3, Activity 5, Polynomial Functions & Their Linear Factors with Answers
1. Graph the lines y = x + 2 and y = x – 4 on the coordinate axes below.
2. Sketch the quadratic function formed by multiplying the linear expressions in #1 on the same
coordinate axes.
3. What do you notice about the x- and y-intercepts of the parabola?
The x-intercepts of the parabola are the same x-intercepts of the lines.
The y-intercept of the parabola is the product of the y-intercepts of the lines.
4. Use the graphs above to complete the sign chart below.
+ 0
- 0
-2
+
0
0
+
+
+
Quadratic function: f(x) = (x + 2)(x – 4)
Linear factor: x - 4
Linear factor: x + 2
4
5. Use the sign chart above to answer the questions below.
a) Is the y value of the quadratic function positive or negative when x = 0?
___negative__
b) Is the y value of the quadratic function positive or negative when x = -7? ___positive___
c) For what values of x is (x + 2)(x – 4) > 0?
_ (-, -2)  (4, )___
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 43
Unit 3, Activity 5, Polynomial Functions & Their Linear Factors with Answers
6. Graph the lines y = x + 1, y = 2 – x, and y = x – 5 on the coordinate axes below
7. Sketch the cubic function formed by multiplying the linear expressions in #1 on the same
coordinate axes.
8. What do you notice about the x- and y-intercepts of the cubic function?
The x-intercepts of the cubic function are the same as the x-intercepts of the lines.
The y-intercept of the cubic function is the same as the product of the y-intercepts
of the lines.
9. Use the graphs above to complete the sign chart below.
+ 0
+
- 0
-1
+
+
0
+ 0
- 0
0 +
2
5
-_
+
+
Cubic function: f(x) = (x + 1)(2 – x)(x - 5)
Linear factor: x - 5
Linear factor: 2 - x
Linear factor: x + 1
10. Use the sign chart above to answer the questions below.
a) Is the y value of the quadratic function positive or negative when x = 13?
negative___
b) Is the y value of the quadratic function positive or negative when x = -2?
positive___
c) For what values of x is (x + 1)(2 – x)(x - 5)  0?
___[-1, 2]  [5, )___
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 44
Unit 3, Activity 7, Applications of Polynomial Functions I
Situation: A farmer has 800 m to enclose a rectangular pen for his goats. If he uses a stream as
one side of the pen, what dimensions will maximize the area of the pen? What is the maximum
area of the pen?
Diagram/Picture
Algebraic Model
Graphical Model
Limitations of the models
Solution
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 45
Unit 3, Activity 7, Applications of Polynomial Functions I with Answers
Situation: A farmer has 800 m to enclose a rectangular pen for his goats. If he uses a stream as
one side of the pen, what dimensions will maximize the area of the pen? What is the maximum
area of the pen?
800 – 2x
Diagram/Picture
x
x
stream
Algebraic Model
Graphical Model
A = x(800 – 2x) or A = 800x – 2x2
Limitations of the models
Side x of the rectangle can only be so large. The domain restriction is 0 < x < 400 m.
The model also assumes that the stream is as long as the side 800 – 2x.
Solution
The dimensions that will maximize the area are 200 m by 400 m.
The maximum area of the rectangular pen is 80,000 m2.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 46
Unit 3, Activity 7, Applications of Polynomial Functions II
Situation: A box, without a top, is to be made from a 20 in by 24 in piece of cardboard by
cutting equal size squares from each corner and then folding up the sides. What size square
should be cut out from each corner in order to maximize the volume? What are the dimensions of
the box? What is the maximum volume?
Diagram/Picture
Algebraic Model
Graphical Model
Limitations of the models
Solution
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 47
Unit 3, Activity 7, Applications of Polynomial Functions II with Answers
Situation: A box, without a top, is to be made from a 20 in by 24 in piece of cardboard by
cutting equal size squares from each corner and then folding up the sides. What size square
should be cut out from each corner in order to maximize the volume? What are the dimensions of
the box? What is the maximum volume?
Diagram/Picture
x
x
x
24 – 2x
x
Algebraic Model
x
x
x
x
20 – 2x
Graphical Model
V = x(24 – 2x)(20 – 2x)
Limitations of the models
The size of the square can only be so big. Domain restrictions are 0 < x < 10 in.
Solution
Square Size:  3.6 in
Dimensions:  3.6 in by 16.8 in by 12.8 in
Maximum Volume:  774.1 in3
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 48
Unit 4, Activity 1, Power Functions – Negative Integer Exponents
Fill in the following modified word grid for y  x p . Start with p = -1 and continue to p = -4.
f(x) = xp
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 49
Unit 4, Activity 1, Power Functions – Negative Integer Exponents with Answers
Fill in the following word grid for y  x p . Start with p = -1 and continue to p = -4.
f(x) = xp
f(x) = x -1
f(x) = x -2
f(x) = x -3
f(x) = x -4
Domain
(-, 0)  (0, )
(-, 0)  (0, )
(-, 0)  (0, )
(-, 0)  (0, )
Range
(-, 0)  (0, )
(0, )
(-, 0)  (0, )
(0, )
Vertical
Asymptote
x=0
x=0
x=0
x=0
Horizontal
Asymptote
y=0
y=0
y=0
y=0
Behavior
as x  
y0
y0
y0
y0
Behavior
as
x  
y0
y0
y0
y0
Extrema
None
None
None
None
Symmetry
Origin
y-axis
Origin
y-axis
Graph
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 50
Unit 4, Activity 6, Applications of Rational Functions
1. The gravitational acceleration (in m/s2) of an object r meters above the earth’s surface
3.987  1014
is g(r) =
.
2
6.378  10 6  r


Question
Answer
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Check
Page 51
Unit 4, Activity 6, Applications of Rational Functions
2. The concentration (in micrograms) of a certain drug in a patient’s bloodstream t hours after
30t
injection is C(t) = 2
.
t  11
Question
Answer
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Check
Page 52
Unit 4, Activity 6, Applications of Rational Functions
3. The daily cost (in thousands of dollars) of manufacturing x sports cars is
C(x) = 0.6x3 – 2.4x2 + 43.2
Question
Answer
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Check
Page 53
Unit 4, Activity 6, Applications of Rational Functions with Answers
1. The gravitational acceleration (in m/s2) of an object r meters above the earth’s surface
3.987  1014
is g(r) =
.
2
6.378  10 6  r


Question
Solution
What is the gravitational
acceleration 1 million meters
above the earth’s surface?
 7.32 m/s2
What is the gravitational
acceleration at
the surface of
the earth?
Check
9.8 m/s2
What are the asymptotes of
this function?
There is no vertical asymptote since the
denominator cannot equal zero. The
horizontal asymptote is y = 0 because the
larger degree is in the denominator.
Use the graph of the function
to determine if it is possible to
escape the pull of gravity.
Since the horizontal asymptote for
the function is y = 0, the gravitational
acceleration for extremely large values of r
will approach but never equal zero. Thus, it
impossible to ever fully escape the pull of
gravity.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 54
Unit 4, Activity 6, Applications of Rational Functions with Answers
2. The concentration (in micrograms) of a certain drug in a patient’s bloodstream t hours after
30t
injection is C(t) = 2
.
t  11
Question
What is the concentration of
the drug 10 hours after
injection?
What happens to the
concentration of the drug as
the time after injection
increases?
Solution
Check
 2.7 micrograms
The concentration decreases as the time
increases. In fact, since the horizontal
asymptote is y = 0, the concentration will
approach 0 as time continues to pass.
Use the graph of the function
to determine when the
concentration of the drug is
highest.
 3.32 hours
What is the highest possible
concentration?
 4.52 micrograms
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 55
Unit 4, Activity 6, Applications of Rational Functions with Answers
3. The daily cost (in thousands of dollars) of manufacturing x sports cars is
C(x) = 0.6x3 – 2.4x2 + 43.2
Question
Write the average cost
function.
What is the average cost of
manufacturing 5 sports cars
per day?
What are the asymptotes for
the average cost function?
Use the graph of the average
cost function to find the
minimum average cost of
manufacturing
a widget.
What is the minimum average
cost per day?
Solution
C ( x) 
Check
0.3x 3  2.4 x 2  43.2
x
$4,140
The vertical asymptote is x = 0.
There is no horizontal or oblique
asymptotes since the degree of the
numerator is 2 larger than the
degree of the denominator.
6 sports cars per day
$3,600
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 56
Unit 5, Activity 1, Power Functions – Fractional Exponents
Fill in the following word grid for y  x p . Start with p = 1/2 and continue to p = 1/5.
f(x) = xp
Graph
Domain
Range
Behavior
as x  
Behavior
as
x  
Extrema
Symmetry
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 57
Unit 5, Activity 1, Power Functions – Fractional Exponents with Answers
Fill in the following word grid for y  x p . Start with p = 1/2 and continue to p = 1/5.
f(x) = xp
f(x) = x1/ 2
f(x) = x1/ 3
f(x) = x1/ 4
f(x) = x1/ 5
Domain
[0, )
(-, )
[0, )
(-, )
Range
[0, )
(-, )
[0, )
(-, )
Behavior
as x  
y
y
y
y
Behavior
as
x  
Does Not Exist
y  -
Does Not Exist
y  -
Extrema
Min (0, 0)
None
Min (0, 0)
None
Symmetry
None
Origin
None
Origin
Graph
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 58
Unit 5, Activity 4, Solving Radical Equations
Use a modified version of the story chain to solve each equation.
Equation
Step
Partner Check
2 x 1 = x
x – 2 = 12  2 x
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 59
Unit 5, Activity 4, Solving Radical Equations
Equation
Step
Partner Check
3x  1 + 3 = x
2 x  3 - x  1 =1
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 60
Unit 5, Activity 4, Solving Radical Equations with Answers
Use a modified version of the story chain to solve each equation.
Equation
Steps May Vary
2 x 1 = x
4(x - 1) = x2
Partner Check
4x – 4 = x2
x2 – 4x + 4 = 0
(x – 2)(x – 2) = 0
x=2
*There is no extraneous root.
x – 2 = 12  2 x
x2 – 4x + 4 = 12 – 2x
x2 – 2x – 8 = 0
(x – 4)(x + 2) = 0
x=4
*x=-2 is an extraneous root
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 61
Unit 5, Activity 4, Solving Radical Equations with Answers
Equation
3x  1 + 3 = x
Step
Partner Check
3x  1 = x - 3
3x + 1 = x2 – 6x + 9
x2 – 9x + 8 = 0
(x – 1)(x – 8) = 0
x=8
*x = 1 is an extraneous root
2 x  3 - x  1 =1
2x  3 = 1 +
x 1
2x + 3 = 1 + 2 x  1 + x + 1
x + 1 = 2 x 1
x2 + 2x + 1 = 2x + 2
x2 - 1 = 0
(x + 1)(x – 1) = 0
x =-1
*x = 1 is an extraneous root
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 62
Unit 5, Activity 6, Pendulum Experiment
Setup
1. Attach string to fishing weight. The lengths should vary from group to group.
2. Place the motion detector facing the path of the pendulum. Make sure that the motion
detector is at least 18 inches from the pendulum. It may help to set the motion detector on
a small stack of books.
3. Plug the motion detector into the Sonic port on the CBL or EA 100.
4. Connect the graphing calculator to the CBL or EA 100.
5. Run the Physics program on the graphing calculator.
6. In the home menu, choose set up probes.
7. Enter 1 for the number of probes.
8. Choose motion.
9. Choose collect data.
10. Choose time graph.
11. Enter 150 measurements at 0.05 second apart.
Procedure
1.
2.
3.
4.
Gently swing the pendulum in the direction of the motion detector.
Press Enter on the calculator to begin taking measurements.
Continue until you see 3-6 periods on the graph.
If you do not get a satisfactory graph, repeat the process until you do.
Data
1. Measure from the top of the string to the middle of the fishing weight to find the length of
the pendulum in inches.
2. Find the period of the pendulum by dividing the total time (in seconds) by the number of
periods.
3. Record your results on the board.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 63
Unit 6, Activity 1, Graphs of Exponential Functions
My
Opinion
Statements
Calculator Findings
Lessons Learned
1. Exponential functions
of the form f(x) = bx are
always increasing.
2. Exponential functions
of the form f(x) = bx
have domains of (-, ).
3. Exponential functions
of the form f(x) = bx
have ranges of (-, ).
4. Exponential
functions of the form
f(x) = bx exhibit
asymptotic behavior.
5. Exponential functions
of the form f(x) = bx
have y-intercepts of 1.
6. Exponential functions
of the form f(x) = bx are
always concave down.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 64
Unit 6, Activity 1, Graphs of Exponential Functions With Answers
My
Opinion
Statements
Calculator Findings
Lessons Learned
1. Exponential functions
of the form f(x) = bx are
always increasing.
False: Exp. functions will
decrease when:
1) 0<b<1 or
2) b>1 with a negative
exponent.
2. Exponential functions
of the form f(x) = bx
have domains of (-, ).
True
3. Exponential functions
of the form f(x) = bx
have ranges of (-, ).
False: Exp. functions of the
form f(x) = bx will have (0, )
as their ranges.
4. Exponential
functions of the form
f(x) = bx exhibit
asymptotic behavior.
True: Exp. functions of the
form f(x) = bx will be
asymptotic to the x-axis.
5. Exponential functions
of the form f(x) = bx
have y-intercepts of 1.
True
6. Exponential functions
of the form f(x) = bx are
always concave down.
False: Exp. Functions of the
form f(x) = bx are always
concave up.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 65
Unit 6, Activity 2, Graphs of Logarithmic Functions
Fill in the following modified word grid. For this grid, b > 1.
f(x) = logb x
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 66
Unit 6, Activity 2, Graphs of Logarithmic Functions With Answers
Fill in the following modified word grid. For this grid, b > 1.
f(x) = logb x
f(x) = log2 x
f(x) = log3 x
f(x) = log x
f(x) = ln x
Exp. Form
2y = x
3y = x
10y = x
ey = x
Asymptote
x=0
x=0
x=0
x=0
Domain
(0, )
(0, )
(0, )
(0, )
Range
(-, )
(-, )
(-, )
(-, )
Increasing
(-, )
(-, )
(-, )
(-, )
Decreasing
Never
Never
Never
Never
Concave Up
Never
Never
Never
Never
Concave
Down
(-, )
(-, )
(-, )
(-, )
x-Intercept
(1, 0)
(1, 0)
(1, 0)
(1, 0)
Graph
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 67
Unit 6, Activity 3, Translations, Dilations, and Reflections of Exponential
Functions
Use technology to complete the chart.
Function
f(x) = 2x-1 - 4
f(x) = -3(1/3)x
f(x) = ½ (4)-x + 1
f(x) = 5e1/3 x
Parent
Translations,
Dilations, &
Reflections
Sketch
Domain
Range
Asymptote
Increasing
Intervals
Decreasing
Intervals
Concavity
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 68
Unit 6, Activity 3, Translations, Dilations, and Reflections of Exponential
Functions With Answers
Use technology to complete the chart.
f(x) = 2x-1 - 4
f(x) = -3(1/3)x
f(x) = ½ (4)-x + 1
f(x) = 5e1/3 x
Parent
f(x) = 2x
f(x) = (1/3)x
f(x) = 4x
f(x) = ex
Translations,
Dilations, &
Reflections
Right 1
Down 4
Reflect over
x-axis; Vertical
stretch of factor 3
Vertical
compression of
factor 2; Reflect
over y-axis; Up 1
Vertical stretch of
factor 5;
Horizontal stretch
of factor 3
Domain
(-, )
(-, )
(-, )
(-, )
Range
(-4, )
(-, 0)
(1, )
(0, )
Asymptote
y = -4
y=0
y=1
y=0
Increasing
Intervals
(-, )
None
None
(-, )
Decreasing
Intervals
None
(-, )
(-, )
None
Concavity
Concave Up
(-, )
Concave Down
(-, )
Concave Up
(-, )
Concave Up
(-, )
Function
Sketch
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 69
Unit 6, Activity 3, Translations, Dilations, and Reflections of Log Functions
Use technology to complete the chart.
Function
f(x)=log2 (x+1)-1
f(x) = -2log1/3 x
f(x) = log (-x) + 3
f(x) = ln (2x)
Parent
Translations,
Dilations, &
Reflections
Sketch
Domain
Range
Asymptote
Increasing
Intervals
Decreasing
Intervals
Concavity
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 70
Unit 6, Activity 3, Translations, Dilations, and Reflections of Log Functions
With Answers
Use technology to complete the chart.
Function
f(x)=log2 (x+1)-1
f(x) = -2log1/3 x
f(x) = log (-x) + 3
f(x) = ln (2x-4)
f(x) = log2 x
f(x) = log1/3 x
f(x) = log x
f(x) = ln x
Left 1
Down 1
Reflect over
x-axis; Vertical
stretch of factor 2
Reflect over
y-axis; Up 3
Horizontal
compression of
factor 2; Right 2
Domain
(-1, )
(0, )
(-, 0)
(0, )
Range
(-, )
(-, )
(-, )
(-, )
Asymptote
x = -1
x=0
x=0
x=2
Increasing
Intervals
(-, )
(-, )
None
(-, )
Decreasing
Intervals
None
None
(-, )
None
Concavity
Concave Down
(-1, )
Concave Up
(0, )
Concave Down
(-, 0)
Concave Down
(0, )
Parent
Translations,
Dilations, &
Reflections
Sketch
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 71
Unit 6, Activity 5, Solving Logarithmic Equations
1.
1.
2.
3.
4.
log 3 (x2 - 6x) = 3
Steps – Incorrect Order
(x – 9)(x + 3) = 0
x2 – 6x – 27 = 0
x=9
3
3 = x2 – 6x
2.
log 4 (x2 + 6x) = 2
4.
log 2 (x – 8) + log 2 (x – 1) = 3
1.
2.
3.
4.
5.
Steps – Incorrect Order
x2 – 9x = 0
log 2 (x2 – 9x + 8) = 3
x=9
3
2 = x2 – 9x + 8
x(x – 9) = 0
5.
log 4 (x – 4) – log 4 (9x + 6) = -2
Steps – Correct Order
3.
log 7 (2x - 9) = - 1
Steps – Correct Order
6.
log 5 (2x + 7) - log 5 (x – 1) = log 5 3
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 72
Unit 6, Activity 5, Solving Logarithmic Equations
7.
1.
2.
3.
4.
2 ln x – 3 ln 2 = ln 18
Steps – Incorrect Order
x2
ln
= ln 18
8
x = 12
Steps – Correct Order
x2
= 18
8
ln x2 – ln 23 = ln 18
5.
x2 = 144
8.
3 log x + log 2 – log 5 = log 50
10. log 2 4 – 1/3 log 2 x = -4
9. ½ log 3 x + 2 log 3 3 = 4
11. 2/3 log 9 x – 3/2 log 9 4 = log 9 18
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 73
Unit 6, Activity 5, Solving Logarithmic Equations with Answers
1.
log 3 (x2 - 6x) = 3
Steps – Incorrect Order
(x – 9)(x + 3) = 0
x2 – 6x – 27 = 0
x=9
3
3 = x2 – 6x
1.
2.
3.
4.
2.
log 4 (x2 + 6x) = 2
Steps – Correct Order
33 = x2 – 6x
2
x – 6x – 27 = 0
(x – 9)(x + 3) = 0
x=9
3.
42 = x2 + 6x
16 = x2 + 6x
x2 + 6x – 16 = 0
(x + 8)(x – 2) = 0
x = -8 x = 2
log 7 (2x - 9) = - 1
7-1 = 2x - 9
1/7 = 2x - 9
64/7 = 2x
x = 32/7
The only solution is x = 2 because -8 is
not in the domain of the log function.
4.
log 2 (x – 8) + log 2 (x – 1) = 3
1.
2.
3.
4.
5.
Steps – Incorrect Order
x2 – 9x = 0
log 2 (x2 – 9x + 8) = 3
x=9
23 = x2 – 9x + 8
x(x – 9) = 0
5.
log 4 (x – 4) – log 4 (9x + 6) = -2
x4
= -2
9x  6
x4
4-2 =
9x  6
1
x4

16 9 x  6
9x + 6 = 16x – 64
70 = 7x
10 = x
log 4
Steps – Correct Order
log 2 (x2 – 9x + 8) = 3
23 = x2 – 9x + 8
x2 – 9x = 0
x(x – 9) = 0
x=9
6.
log 5 (2x + 7) - log 5 (x – 1) = log 5 3
2x  7
= log 5 3
x 1
2x  7
=3
x 1
log 5
2x + 7 = 3x - 3
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
10 = x
Page 74
Unit 6, Activity 5, Solving Logarithmic Equations with Answers
7.
2 ln x – 3 ln 2 = ln 18
Steps – Incorrect Order
x2
ln
= ln 18
8
x = 12
1.
2.
Steps – Correct Order
ln x2 – ln 23 = ln 18
ln
x2
= 18
8
ln x2 – ln 23 = ln 18
3.
4.
5.
x2 = 144
8.
3 log x + log 2 – log 5 = log 50
log
2x3
= log 50
5
2x3
= 50
5
2x3 = 250
x3 = 125
x=5
10. log 2 4 – 1/3 log 2 x = -1
log 2
4
3
4
-1
2 =
x
3
x
1
4
= 3
2
x
3
x=8
x = 512
x2
= ln 18
8
x2
= 18
8
x2 = 144
x = 12
9. ½ log 3 x + 2 log 3 3 = 4
log 3 9 x = 4
34 = 9 x
81 = 9 x
9= x
81 = x
11. 2/3 log 9 x – 3/2 log 9 4 = log 9 18
2
= -1
log 9
x 3
= log 9 18
8
2
x 3
= 18
8
x2/3 = 144
x = 1443/2
x = 1728
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 75
Unit 6, Activity 6, Exponential Growth & Decay
Create an exponential growth or decay story chain modeled after one of the examples covered in
class.
STORY LINES
AUTHOR
Create three questions based on the story chain.
1.
2.
3.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 76
Unit 6, Activity 6, Money Investments
Create a money investment story chain modeled after one of the examples covered in class.
STORY LINES
AUTHOR
Create three questions based on the story chain.
1.
2.
3.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 77
Unit 6, Activity 7, Loudness of Sound
SQPL Statement: Some sounds can barely be heard; while others can be painful.
Your Questions
Answers
Classmates’ Questions
Answers
1. How many times more intense is a sound of 80 dB than one of 50 dB?
2. How many times more intense is a sound of 115 dB than one of 70 dB?
3. Find the loudness, in decibels, of a washing machine that operates at an intensity of 10-5 watt
per square meter.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 78
Unit 6, Activity 7, Loudness of Sound With Answers
NOTE: Answers will vary. Some important questions are listed below.
SQPL Statement: Some sounds can barely be heard; while others can be painful.
Your Questions
Answers
Classmates’ Questions
Answers
Is the SQPL statement true?
yes
How is sound measured?
Decibels: watts per square meter
What sounds are barely audible?
Whisper: 10 decibels Light Rain: 20 decibels
What sounds are painful?
Jet taking off from 100 ft away: 140 decibels
Shotgun Blast: 140 decibels
How do you use the Decibel Scale?
The scale starts at 0 and counts by 10 up to
140. To compare sounds, find the difference
between their decibels and calculate 10 to that
difference.
Is there a decibel formula?
 x 
L(x) =10 log  12  ; where x is the
 10 
intensity of sound in watts per square meter
Yes,
1. How many times more intense is a sound of 80 dB than one of 50 dB?
80 – 50 = 30 (which is 3 steps on the decibel scale)  103 = 1000 times more intense
2. How many times more intense is a sound of 115 dB than one of 70 dB?
115 – 70 = 45 (which is 4½ steps on the decibel scale)  104.5  31,622.8 times more intense
3. Find the loudness, in decibels, of a washing machine that operates at an intensity of 10-5 watt
per square meter.
 10 5 
L(10 ) = 10 log  12  = 10 log 107 = 70 dB
 10 
-5
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 79
Unit 6, Activity 7, Magnitude of Earthquakes
SQPL Statement: The earthquake with the largest magnitude occurred in the Indian Ocean.
Your Questions
Answers
Classmates’ Questions
Answers
1. The 1906 earthquake in San Francisco had a magnitude of 6.9. The 1985 earthquake in
New Mexico had a magnitude of 8.1. Compare the intensities of the two earthquakes.
2. Find the magnitude of an earthquake whose seismographic reading is 10 mm at a distance of
100 km from the epicenter.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 80
Unit 6, Activity 7, Magnitude of Earthquakes with Answers
NOTE: Answers will vary. Some important questions are listed below.
SQPL Statement: The earthquake with the largest magnitude occurred in the Indian Ocean.
Your Questions
Answers
Classmates’ Questions
Answers
Is the SQPL statement true?
No, the earthquake with the largest magnitude
occurred in Chile. It measured a 9.5 on the
Richter Scale.
How is magnitude measured?
The logarithmic ratio of the seismographic
reading of the earthquake that occurred to the
zero-level earthquake whose seismographic
reading is 10-3 at a distance of 100km from the
epicenter.
How do you use the Richter Scale?
The Richter Scale is used to compare the
magnitudes of earthquakes. Since it is logarithmic
in nature, each whole number increase in Richter
value represents a ten-fold increase in magnitude.
What was the worst earthquake in US history?
San Francisco, April 18, 1906
Magnitude = 7.9
Is there a formula for determining the
magnitude of an earthquake?
 x 
 ; where x is the
Yes, M(x) = log 
 10  3 
seismographic reading in millimeters 100 km
from the epicenter
1. The 1906 earthquake in San Francisco had a magnitude of 6.9. The 1985 earthquake in
New Mexico had a magnitude of 8.1. Compare the intensities of the two earthquakes.
8.1 – 6.9 = 1.2 (which is 1.2 steps on the Richter Scale)  101.2 15.85 times more intense
2. Find the magnitude of an earthquake whose seismographic reading is 10 mm at a distance
of 100 km from the epicenter.
 10 
M(10) = log  3  = log (104) = 4
 10 
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 81
Unit 6, Activity 8, Linearizing Exponential Data
1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year
Population 92.0 105.7 122.8 131.7 150.7 179.3 203.3 226.5 246.8 281.4
(millions)
1. Enter the year 1910 as 1, 1920 as 3, and so on.
2. Which of the following models best fits the data? Justify your answer!
Linear
Power
Exponential
3. Write the equation of the model of best fit.
4. Linearize the data. Show your work!
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 82
Unit 6, Activity 8, Linearizing Exponential Data With Answers
1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year
Population 92.0 105.7 122.8 131.7 150.7 179.3 203.3 226.5 246.8 281.4
(millions)
1. Enter the year 1910 as 1, 1920 as 3, and so on.
2. Which of the following models best fits the data? Justify your answer!
Linear: r  .9909
Power:
r  .9559
Exponential:
r  .9980
*Since this model had the largest correlation coefficient, it is
the best fit for this data.
3. Write the equation of the model of best fit.
y  82.423(1.1325)x
4. Linearize the data. Show your work!
m = log (1.1325)  .0540
b = log (82.423)  1.9160
y  0.540x + 1.9160
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 83
Unit 7, Activity 1, Vocabulary Cards
Def: the study of collecting,
organizing, and interpreting data
STATISTICS
Ex: Statistics are used to
determine car insurance rates.
Def: a person or object in the
study
INDIVIDUAL
VARIABLE
Ex: If a study is about teachers,
each teacher interviewed or
observed is called an individual.
Def: the characteristic of the
individual to be observed or
measured
Ex: test scores
QUANTITATIVE
VARIABLE
QUALITATIVE
VARIABLE
Def: variable that quantifies
(assigns a numerical value)
Ex: a person’s weight
Def: variable that categorizes or
describes
Ex: gender
Def: every individual of interest
POPULATION
Ex: all living presidents – not
just a few of them
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 84
Unit 7, Activity 1, Vocabulary Cards
SAMPLE
Def: a subset of the population
(some of the individuals of
interest)
Ex: some living presidents
NOMINAL
DATA
Def: data consisting of only
names or qualities – no numerical
values
Ex: colors
ORDINAL
DATA
INTERVAL
DATA
Def: data that has an order but
differences between data values
are meaningless
Ex: student high school rankings
1st, 9th , 28th , etc.
Def: data that has an order,
meaningful differences, but may
or may not have a starting point
which makes ratios meaningless
Ex: temperature readings
RATIO
DATA
Def: data with the same
characteristics as interval data but
with a starting point which makes
ratios meaningful
Ex: measures of height
DESCRIPTIVE
STATISTICS
Def: the practice of collecting,
organizing, and summarizing
information from samples or
populations
Ex: graphs, measures of center
and spread
INFERENTIAL
STATISTICS
Def: the practice of interpreting
sample values gained from
descriptive techniques and
drawing conclusions about the
population
Ex: polling 100 voters and using
the results to predict a winner
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 85
Unit 7, Activity 2, Collecting and Organizing Univariate Data
1. Collect data on the number of siblings for each student in the class. Identify the data set as
a sample or a population.
2. Organize the data using a box-whisker plot.
3. Organize the data using the display of your choice.
4. Organize the data using another display of your choice.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 86
Unit 7, Activity 2, Collecting and Organizing Univariate Data with Answers
1. Collect data on the number of siblings for each student in the class. Identify the data set as a
sample or a population.
Copy the data from one of the students so that you can create the same
graphs as the students.
The data set is from a population since the number of siblings was collected
from each student in the class
2. Organize the data using a box-whisker plot.
The box-whisker plot cannot be provided since it will depend on the data
collected in class.
3. Organize the data using the display of your choice.
Displays will vary.
4.
Organize the data using another display of your choice.
Displays will vary.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 87
Unit 7, Activity 2, Data Displays: Advantages and Disadvantages
Complete the modified word grid below.
Type of Graph
Advantages
Disadvantages
Line Plot
Bar Graph
Circle Graph
Stem-Leaf Plot
Box Plot
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 88
Unit 7, Activity 2, Data Displays: Advantages and Disadvantages with Answers
Complete the modified word grid below.
Type of Graph
Advantages
Individual data is not lost
Line Plot
Easy to create
Shows range, minimum, maximum,
gaps, clusters, & outliers
Disadvantages
Can be cumbersome if there are a
large number of data values
Needs a small range of data
Easy to create
Only used for discrete data
Bar Graph
Easy to read
Individual data is lost
Makes comparisons easy
Only used for discrete data
Easy to read
Circle Graph
Shows percentages
Individual data is lost
Good for only about 3-7 categories
Total is often missing
Easy to create
Stem-Leaf Plot
Stores a lot of data in a
smaller space
Shows range, minimum, maximum,
gaps, clusters, & outliers
Can be cumbersome if there are a
large number of data values
Can be difficult to read
Not visually appealing
Identifies outliers
Box Plot
Makes comparisons easy
Shows 5-point summary
(minimum, maximum, 1st Quartile,
Median, & 3rd Quartile)
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Individual data is lost
Can be confusing to read
Not visually appealing
Page 89
Unit 7, Activity 3, Frequency Tables and Histograms
The average lengths of the North American geese and ducks are given below.
Name of Bird
Fulvous Whistling Duck
White-fronted Goose
Ross’ Goose
Canada Goose (small)
Wood duck
American Black Duck
Mallard
Northern Pintail (female)
Cinnamon Teal
Gadwall
American Wigeon
Redhead
Tufted Duck
Lesser Scaup
King Eider
Oldsquaw (male)
Black Scoter
White-winged Scoter
Barrow’s Goldeneye
Hooded Merganser
Red-breasted Merganser
Masked Duck
Class
Lower Limit Upper Limit
Average
Length
50 cm
72 cm
61 cm
61 cm
69 cm
52 cm
59 cm
55 cm
40 cm
50 cm
52 cm
51 cm
43 cm
42 cm
55 cm
52 cm
48 cm
55 cm
47 cm
44 cm
57 cm
33 cm
Name of Bird
Black-bellied Whistling Duck
Snow Goose
Brant
Canada Goose (large)
Green-winged Teal
Mottled Duck
Northern Pintail (male)
Blue-winged Teal
Northern Shoveler
Eurasian Wigeon
Canvasback
Ring-necked Duck
Greater Scaup
Common Eider
Harlequin Duck
Oldsquaw (female)
Surf Scoter
Common Goldeneye
Bufflehead
Common Merganser
Ruddy Duck
Number of birds
or Frequency
Relative
Frequency =
f
; n  43
n
Average
Length
53 cm
74 cm
66 cm
101 cm
35 cm
53 cm
69 cm
39 cm
47 cm
49 cm
55 cm
41 cm
45 cm
64 cm
44 cm
41 cm
48 cm
46 cm
35 cm
63 cm
39 cm
Cumulative
Relative
Frequency
≤x<
≤x<
≤x<
≤x<
≤x<
≤x<
≤x<
≤x<
≤x<
≤x≤
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 90
Unit 7, Activity 3, Frequency Tables and Histograms with Answers
Class
Lower Limit Upper Limit
33 ≤ x < 40
40 ≤ x < 47
47 ≤ x < 54
54 ≤ x < 61
61 ≤ x < 68
68 ≤ x < 75
75 ≤ x < 82
82 ≤ x < 89
89 ≤ x < 96
96 ≤ x ≤ 103
Number of birds
or Frequency
5
9
13
6
5
4
0
0
0
1
Relative
Frequency =
f
; n  43
n
.12
.21
.30
.14
.12
.09
0
0
0
.02
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Cumulative
Relative
Frequency
.12
.21 + .12 = .33
.30 + .33 = .63
.14 + .63 = .77
.77 + .12 = .89
.09 + .89 = .98
.98
.98
.98
.02 + .98 = 1.00
Page 91
Unit 7, Activity 3, Frequency Tables and Histograms with Answers
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 92
Unit 7, Activity 3, Math Test Grades
Math Test Grades (0-100 pts)
Student
Alvin
Amy
Brett
Cedric
Charles
Connie
Debra
Dexter
Diane
Dion
Edrick
Evan
Fredrick
Grace
Gregory
Hakim
Helen
Janice
Jay
Jose
Test Grade
83
59
90
88
66
52
79
36
77
85
83
91
99
80
85
88
69
71
76
99
Student
Kay
Keller
Kim
Lamar
Lance
Lee
Leon
Mai
Mason
Nicole
Ouida
Pablo
Penny
Patrice
Patrick
Pedro
Stephanie
Trevor
Tyler
Xavier
Test Grade
42
93
84
77
63
78
91
95
76
84
80
77
80
86
88
92
55
66
78
81
Complete the table.
Class
Lower Limit Upper Limit
Number of scores
or Frequency
Relative
Frequency =
f
; n  43
n
Cumulative
Relative
Frequency
Draw a relative frequency histogram on the back of this BLM.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 93
Unit 7, Activity 3, Math Test Grades with Answers
Class
Lower Limit Upper Limit
Number of scores
or Frequency
36 ≤ x < 44
44 ≤ x < 52
52 ≤ x < 60
60 ≤ x < 68
68 ≤ x < 76
76 ≤ x < 84
84 ≤ x < 92
92 ≤ x < 100
2
0
3
3
2
14
11
5
Relative
Frequency =
f
; n  43
n
.05
0
.075
.075
.05
.35
.275
.125
Cumulative
Relative
Frequency
.05
.05+0=.05
.075+.05=.125
.075+.125=.20
.05+.20=.25
.35+.25=.60
.275+.60=.875
.125+.875=1.00
Relative Frequency Histogram
.35
.30
.25
.20
.15
.10
.05
92≤x<100
84≤x<92
76≤x<84
68≤x<76
60≤x<68
52≤x<60
44≤x<52
36≤x<44
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 94
Unit 7, Activity 4, Tropical Cyclones
Year
1991
Last Named
Tropical
Cyclone
Grace
Number of Total Number
Hurricanes of Tropical
Cyclones
3
Date of First
Tropical
Cyclone
June 29
Date of Last
Tropical
Cyclone
October 28
1992
Frances
4
August 16
October 22
1993
Harvey
4
June 18
September 18
1994
Gordon
3
June 30
November 8
1995
Tanya
11
June 3
October 27
1996
Marco
9
June 17
November 18
1997
Grace
3
June 30
October 16
1998
Nicole
10
July 27
November 24
1999
Lenny
8
June 11
November 13
2000
Nadine
8
August 4
October 19
2001
Olga
9
June 5
November 24
2002
Lili
4
July 14
October 14
2003
Peter
7
April 21
December 9
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 95
Unit 7, Activity 6, Distribution Shapes
Complete the chart by matching the name, definition, and example of data from the next
page with its appropriate shape.
Example Shape of
Histogram
Name and Definition
Example of Data
A.
B.
C.
D.
E.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 96
Unit 7, Activity 6, Distribution Shapes
Names & Definitions
1. Symmetrical, normal or triangular – both sides of the distribution are identical. Also called a
bell-shaped distribution.
2. Left skewed or negatively skewed – the tail is to the left
3. Bi-modal – the two classes with the highest frequencies are separated by at least one class
4. Right skewed or positively skewed – the tail is to the right.
5. Uniform or rectangular – the bars are all the same height
Examples of Data
I. Heights of a group of people containing both males and females
II. Heights of a group of males
III. Grades on a test where most students perform poorly
IV. Ages of people getting their first driver’s license
V. Rolls of a regular die
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 97
Unit 7, Activity 6, Distribution Shapes with Answers
Example Shape of
Histogram
Name and Definition
Example of Data
A.
3. Bi-modal – the two
classes with the highest
frequencies are separated
by at least one class
I. Heights of a group of
people containing both
males and females
B.
2. Left skewed or negatively
skewed – the tail is to the
left
IV. Grades on a test in
which most students do
fairly well
C.
5. Right skewed or positively
skewed – the tail is to the
right
III. Ages of people getting
their first driver’s
license
D.
4. Uniform or rectangular –
the bars are all the same
height
V. Rolls of a regular die
E.
1. Symmetrical, normal or
triangular – both sides of
the distribution are
identical. Also called a
bell-shaped distribution.
II. Heights of a group of
males
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 98
Unit 7, Activity 7, Normal Distribution
Describe why each distribution is not normal.
1.
2.
3.
4.
5. Draw and label a normal distribution for exam grades (0-100 pts) if the mean is 78 and the
standard deviation is 5.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 99
Unit 7, Activity 7, Normal Distribution
6. Determine the number of standard deviations either above or below the mean for an exam
score of 68.
7. What is the probability that a student scored between 88 and 93 pts?
8. What is the probability that a student scored at least a 73?
9. If 160 students took the exam, how many got a C using the grading scale 78-88 pts.
10. What is the probability that a student scored a 90?
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 100
Unit 7, Activity 7, Normal Distribution with Answers
Describe why each distribution is not normal.
1.
The curve crosses the horizontal
axis.
2.
The curve is not symmetrical
about the mean.
3.
The curve has two peaks and is
not bell-shaped. Thus, the
highest point does not lie
directly above the mean.
4.
The end behavior of the curve
does not follow the horizontal
axis.
5. Draw and label a normal distribution for exam grades (0-100 pts) if the mean is 78 and the
standard deviation is 5.
63 68 73 78 83 88 93
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 101
Unit 7, Activity 7, Normal Distribution with Answers
6. Determine the number of standard deviations either above or below the mean for an exam
score of 68.
68 is two standard deviations below the mean
7. What is the probability that a student scored between 88 and 93 pts?
2.35%
8. What is the probability that a student scored at least a 73?
.34 + .34 + .135 + .0235 +.0015 = .84
or
84%
OR
1 - .135 - .0235 - .0015 = .84
or
84%
9. If 160 students took the exam, how many got a C using the grading scale 78-88 pts.
160  .475 = 76 students
10. What is the probability that a student scored a 90?
z=
95  78
= 2.4
5
Reading the Z-table, the probability is 49.2%.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 102
Unit 8, Activity 1, Bivariate Vocabulary Cards
Def: a graphical display of the
pairs of values of two variables
SCATTERPLOT

Height
Ex:



age
Def: a relationship between two
variables
CORRELATION
CORRELATION
COEFFICIENT
Ex: number of calories eaten and
a person’s weight
Def: a number (r) from -1 to 1 that
measures the linear relationship between
two variables
Ex: the number of movie tickets sold
and the total cost is a perfect
Linear relationship; thus, the correlation
coefficient would be 1
Def: a number that measures the proportion
COEFFICIENT OF
DETERMINATION
RESIDUAL
of variance in the response variable explained by the regression line and explanatory
variable (0 r2  1)
Ex: an r2 value of .70 indicates that 70% of
the variance in the response variable can be
accounted for by the explanatory variable
Def: the difference between the
observed value and the value
suggested by the regression line

Ex: y - y
REGRESSION
LINE
Def: line that describes how the
response variable changes as the
explanatory variable changes

Height

Ex:


age
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 103
Unit 8, Activity 1, Bivariate Vocabulary Cards
LEAST SQUARES
LINE
EXPLANATORY
VARIABLE
RESPONSE
VARIABLE
Def: line that makes the sum of
squares of the vertical distances
of the data points from the line as
small as possible

Ex: y = a + bx
Def: the independent variable
which is used as a predictor of the
response variable
Ex: number of calories eaten
Def: the dependent or predicted
variable
Ex: a person’s weight
Def: to infer or estimate by extending
or projecting known information
EXTRAPOLATION
Ex: known independent variable data
ranges from 0-50 and a prediction is
made for an independent value of 60
Def: inferring or estimating a value that
lies between known values
INTERPOLATION
CAUSATION
Ex: known independent variable data
ranges from 0-50 and a prediction is
made for an independent value of 40
Def: the relationship between a
cause and its effect which can only
be determined by conducting an
experiment
Ex: experimental studies have
shown that smoking causes lung
cancer
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 104
Unit 8, Activity 2, Scatterplots and Correlations
Label each scatterplot as a perfect positive correlation, perfect negative correlation, strong
positive correlation, strong negative correlation, weak positive correlation, weak negative
correlation, or no correlation.
1.
2.
3.
4.
5.
6.
7.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 105
Unit 8, Activity 2, Scatterplots and Correlations with Answers
Label each scatterplot as a perfect positive correlation, perfect negative correlation, strong
positive correlation, strong negative correlation, weak positive correlation, weak negative
correlation, or no correlation.
1.
2.
perfect positive
correlation
4.
3.
strong positive
correlation
weak negative
correlation
5.
strong negative
correlation
6.
weak positive
correlation
7.
perfect negative
correlation
no correlation
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 106
Unit 8, Activity 2, Regression Line and Correlation
Step One
Go to the following web site: http://illuminations.nctm.org/LessonDetail.aspx?ID=L456 .
Step Two
Use the interactive math applet below to help you answer these questions:
1. Compare the r-values for the following three situations.
a) Create a scatterplot that you think shows a strong positive linear association between
the two variables. What is the r-value? Draw the regression line.
b) Create a scatterplot that you think shows a strong negative linear association between
the two variables. What is the r-value? Draw the regression line.
c) Create a scatterplot that you think shows no linear association between the two
variables. What is the r-value?
2. For each r-value below, create a scatterplot that has that exact r-value.
a) r = 1
b) r = -1
c) r = 0
3. Plot several points that exhibit a strong positive linear trend, and then plot one outlier.
a) Overall, is this scatterplot roughly linear? b) Is the r-value close to 1?
4. In the lower left corner of the coordinate plane, plot 10 points that exhibit no trend (this
is sometimes called a "cloud" of points). Then plot one point in the upper right corner.
a) Overall, is this scatterplot linear?
b) Is the r-value close to 1?
5. a) Does a high r-value necessarily mean that the data are definitely linear?
b) Does an r-value close to zero always mean that the data are not linear?
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 107
Unit 8, Activity 2, Regression Line and Correlation with Answers
Step One
Go to the following web site: http://illuminations.nctm.org/LessonDetail.aspx?ID=L456 .
Step Two
Use the interactive math applet below to help you answer these questions:
1. Compare the r-values for the following three situations.
a) Create a scatterplot that you think shows a strong positive linear association between
the two variables. What is the r-value? Draw the regression line.
r values will vary, but should be close to 1
b) Create a scatterplot that you think shows a strong negative linear association between
the two variables. What is the r-value? Draw the regression line.
r values will vary, but should be close to -1
c) Create a scatterplot that you think shows no linear association between the two
variables. What is the r-value?
r values will vary, but should be close to 0
2. For each r-value below, create a scatterplot that has that exact r-value.
a) r = 1
b) r = -1
c) r =0
points make a straight
points make a straight
points randomly scattered
line with a positive slope line with a negative slope
with no linear pattern
3. Plot several points that exhibit a strong positive linear trend, and then plot one outlier.
a) Overall, is this scatterplot roughly linear? b) Is the r-value close to 1?
The farther the outlier is from the
The farther the outlier is from the
rest of the data, the less linear the
rest of the data, the farther the
relationship.
r-value is from 1.
4.
In the lower left corner of the coordinate plane, plot 10 points that exhibit no trend (this
is sometimes called a "cloud" of points). Then plot one point in the upper right corner.
a) Overall, is this scatterplot linear?
no
b) Is the r-value close to 1?
yes
5. a) Does a high r-value necessarily mean that the data are definitely linear?
no
b) Does an r-value close to zero always mean that the data are not linear?
no - The moral is that the correlation coefficient, r, is a valuable tool for
studying the linear association between two variables, but it does not fully explain
the association (in fact, no statistic does).
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 108
Unit 8, Activity 2, RAFT Writing
Student example of RAFT writing in math.
R – A whole number between 1 and 9
A – A whole number equal to 10 minus the number used (from R)
F – A letter
T – Why it is important to be a positive role model for the fractions less than one.
Dear Number 7,
It has come to my attention that you are not taking seriously your responsibilities as a role
model for the fractions. With this letter I would like to try to convince you of the importance of
being a positive role model for the little guys. Some day, with the proper combinations, they, too,
will be whole numbers. It is extremely important for them to understand how to properly carry
out the duties of a whole number. For them to learn this, it is imperative for them to have good
positive role models to emulate. Without that, our entire numbering system could be in ruins.
They must know how to respond if ever asked to become a member of a floating point gang.
Since they are not yet whole, it is our duty to numberkind to make sure they are brought up
properly to the left of the decimal.
Thank you in advance for your support,
The number 3
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 109
Unit 8, Activity 3, Least Squares Line
1. Which line seems to best fit the data?
Possible line 1
Possible line 2
Possible line 3
2. Complete the chart.
Cost of Living
Index
Average Annual
Pay
x
y
San Francisco,
CA
169.8
56,602
Washington, D.C.
138.8
48,430
Houston, TX
91.6
42,712
Atlanta, GA
97.6
41,123
Huntsville, AL
91.8
38,571
Saint Louis, MO
101.3
36,712
Brazoria, TX
90.5
36,253
Memphis, TN
90.7
35,922
City
x2
xy
SUM
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 110
Unit 8, Activity 3, Least Squares Line

3. Calculate the least squares line y = a + bx using the formulas below.
b=
SS xy
SS x
;
 x  y 
SSxy =  xy 
n
 x 

2
SSx =
x
2
n
a = y  b x ( y and x are the means for each respective variable)
4. Compare the least squares line from number 3 with the least squares line generated by the
graphing calculator.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 111
Unit 8, Activity 3, Least Squares Line
5. Using the calculator’s least squares, state the real-life meaning of the slope and y-intercept.
6. Use the calculator’s least squares line to find the average annual salary for a city with a cost
of living index of 100.
7. Use the calculator’s least squares line to find the average annual salary for a city with a cost
of living index of 80.
8. State limitations of the linear model.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 112
Unit 8, Activity 3, Least Squares Line with Answers
1. Which line seems to fit the data the best?
Possible line 1
Possible line 2
Possible line 3
Line #1 appears to have the smallest vertical distances between the data points and the
line of best fit. Therefore, its sum of squares will be smaller than that of the other two lines.
2. Complete the chart.
Cost of Living
Index
Average Annual
Pay
x
y
x2
xy
San Francisco,
CA
169.8
56,602
28832.04
9611019.6
Washington, D.C.
138.8
48,430
19265.44
6722084
Houston, TX
91.6
42,712
8390.56
3912419.2
Atlanta, GA
97.6
41,123
9525.76
4013604.8
Huntsville, AL
91.8
38,571
8427.24
3540817.8
Saint Louis, MO
101.3
36,712
10261.69
3718925.6
Brazoria, TX
90.5
36,253
8190.25
3280896.5
Memphis, TN
90.7
35,922
8226.49
3258125.4
SUM
872.1
336,325
101119.47
38057892.9
City
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 113
Unit 8, Activity 3, Least Squares Line with Answers

3. Calculate the least squares line y = a + bx using the formulas below.
SSxy =
 xy 
 x  y 
872.1336,325 = 1,394,263.838
= 38,057,892.98
n
 x 

2
SSx =
b=
x
SS xy
SS x
2
=
n
= 101,119.47-
872.12  6,049.66875
8
1,394,263.938
 230.5
6,049.66875
a = y  bx =
336,325
8
 872.1 
 230.5
  16,913.2
 8 

y  16913.2 + 230.5x
4. Compare the least squares line from number 3 with the least squares line generated by the
graphing calculator.
Calculator’s least squares line: y  16,916.6 + 230.5x
The slopes are identical, but the y-intercepts vary by 3.4.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 114
Unit 8, Activity 3, Least Squares Line with Answers
5. Using the calculator’s least squares, state the real-life meaning of the slope and y-intercept.
Slope: For each increase of 1 in the cost of living index, the average annual salary
will increase by $230.50
y-intercept: For a cost of living index of 0, the average annual salary would be
$16,916.6 Note: The y-intercept is meaningless for this particular
data set since the cost of living index will never equal zero.
6. Use the calculator’s least squares line to find the average annual salary for a city with a cost
of living index of 100.

y  16,916.6 + 230.5(100)  $39,966.6
7. Use the calculator’s least squares line to find the average annual salary for a city with a cost
of living index of 80.

y  16,916.6+ 230.5(80)  35,356.60
8. State limitations of the linear model.
Answers will vary. One possible limitation is that there are many factors that affect
the average annual salary for a particular city (population, industries, unemployment index, etc.).
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 115
Unit 8, Activity 3, Hospitals
State
Alabama
Alaska
Mississippi
Ohio
Oklahoma
Louisiana
Utah
California
Texas
Maine
Population (in millions)
4.501
0.649
2.881
11.436
3.512
4.496
2.351
35.484
22.119
1.306
Number of hospitals
106
19
91
168
105
128
42
464
383
37
1. Is a linear model appropriate for this data set? Justify your answer.
2. Calculate the least squares line.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 116
Unit 8, Activity 3, Hospitals
3. Give the real-life meaning of the slope and y-intercept.
4. Use your regression line to predict the number of hospitals for a city with a population of 6
million people. Is this an example of interpolation or extrapolation?
5. State limitations of the model.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 117
Unit 8, Activity 3, Hospitals with Answers
State
Alabama
Alaska
Mississippi
Ohio
Oklahoma
Louisiana
Utah
California
Texas
Maine
Population (in millions)
4.501
0.649
2.881
11.436
3.512
4.496
2.351
35.484
22.119
1.306
Number of hospitals
106
19
91
168
105
128
42
464
383
37
1. Is a linear model appropriate for this data set? Justify your answer.
The scatterplot reveals a positive linear relationship since the number of hospitals
continues to increase by about the same amount as the population increases.
2. Calculate the least squares line.
SSxy =
 xy 
 x  y 
88.7351543 = 15,008.4205
=28,700.321 -
 x 

2
SSx =  x
b=
SS xy
SS x
2
=
10
n
n
=1,947.90787 -
88.7352 = 1,160.517848
10
15,008.4205
 12.93252019
1,160.517848
a = y  b x =154.3 – 12.93252019(8.8735)  39.54328209

y  39.54328209 + 12.93252019x
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 118
Unit 8, Activity 3, Hospitals with Answers
3. Give the real-life meaning of the slope and y-intercept.
Slope: For every increase of 1 million people, there are approximately 11 more
hospitals.
y-intercept: For a population of 0, there are about 48 hospitals. This does not make
sense for this data set.
4. Use your regression line to predict the number of hospitals for a city with a population of 6
million people. Is this an example of interpolation or extrapolation?

y  39.54328209 + 12.93252019(6)  117 hospitals
This is an example of interpolation since 6 million people lies within the given range of
the independent variable.
5. State limitations of the model.
Limitations will vary.
Ex. Linear extrapolation can be misleading because there is a chance that the linear
tendency might level off for larger data values. Also, the size of the hospitals is not
known. A few large hospitals could service the same number of people as a large
number of small hospitals.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 119
Unit 8, Activity 4, Correlation Coefficient and Coefficient of Determination
Year
2000
2001
2002
2003
2004
Number of students in the United States
who took the AP Statistics Exam
34118
41609
49824
58230
65878
1. Calculate the correlation coefficient using the appropriate formulas.
2. Calculate the coefficient of determination and interpret its meaning.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 120
Unit 8, Activity 4, Correlation Coefficient and Coefficient of Determination with
Answers
Year
Number of students in the United States
who took the AP Statistics Exam
34118
41609
49824
58230
65878
2000
2001
2002
2003
2004
1. Calculate the correlation coefficient using the appropriate formulas.
r=
SS xy
SS x SS y
SS xy =  xy SS x =  x 2 SS y =  y 2 -
(  x )(  y )
(x)
n
= 499897459 -
2
n
(  y)2
= 20040030 -
10010× 249659
= 80141
5
10010 2
= 10
5
= 1.310842157×10 10 -
n
80141
r=
= .9998
10×642498308.8
249659 2
= 642498308.8
5
2. Calculate the coefficient of determination and interpret its meaning.
r2 = .9996
The coefficient of determination states that approximately 99.96% of the variance in the
number of U.S. high school students taking the AP statistics exam can be accounted for
by the year. Thus, the number of years can accurately be used to explain the number of
students taking the exam.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 121
Unit 8, Activity 5, Residual Plots
1. Which residual plot states that the linear regression model is a good fit? Explain your answer.
a)
b)
Height (cm)
Arm Span (cm)
95
95.5
c)
106
100
120
107
133
122.5
150
128
162
136
166
137.5
174
145.5
2. Draw the scatterplot using the graphing calculator. What type of model appears to be a good
fit for the data? Explain your answer.
3. Write the linear regression equation and interpret the meaning of the slope and y-intercept.
4. Record and interpret the correlation coefficient and coefficient of determination.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 122
Unit 8, Activity 5, Residual Plots
5. Draw and label the residual plot.
6. What does the residual plot tell you about the data?
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 123
Unit 8, Activity 5, Residual Plots with Answers
1. Which residual plot states that the linear regression model is a good fit? Explain your answer.
a)
b)
c)
Residual plot b demonstrates that a linear regression model is a good fit because the
points are randomly dispersed.
Height (cm)
Arm Span (cm)
95
95.5
106
100
120
107
133
122.5
150
128
162
136
166
137.5
174
145.5
2. Draw the scatterplot using the graphing calculator. What type of model appears to be a good
fit for the data? Explain your answer.
A linear model appears to be a good fit since the data points are increasing at
about the same rate.
3. Write the linear regression equation and interpret the meaning of the slope and y-intercept.
y  34.2542971 + 0.63107199x
m  0.631 which means that for every cm of height, the arm span increases by about
0.631 cm
b  34.25 ; which means that for a height of 0 cm, the arm span would be about 34.25
cm (The interpretation for b does not make sense for this data set.)
4. Record and interpret the correlation coefficient and coefficient of determination.
r  0.99259244 ; which indicates a strong positive linear relationship
r2  0.98523975 ; which indicates that about 98.52% of the variation in arm span can
be accounted for by the explanatory variable height
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 124
Unit 8, Activity 5, Residual Plots with Answers
5. Draw and label the residual plot.
Residuals
5
4
3
2
1
0
-1
-2
-3
-4
-5







Height (cm)
90
100
110
120
130
140
150
160
170
180
6. What does the residual plot tell you about the data?
Since the points are randomly dispersed, a linear model is appropriate for this
data set.
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 125
Unit 8, Activity 6, Achieving Linearity
Display the following information on a poster board. If necessary, use both sides of the poster
board.
1. Collect and record data on two variables that you think are linearly related. Be sure to include
units and at least eight values for each variable.
2. Draw and label a scatterplot of the raw data.
3. Does a linear model appear to be a good fit for the raw data? Explain your answer.
4. Find the linear regression equation using the graphing calculator.
5. Interpret the real-life meaning of the slope and y-intercept.
6. Record and interpret the correlation coefficient and coefficient of determination.
7. Draw the residual plot for the raw data.
8. What does the residual plot say about the fit of the linear model?
9. Does the graphical analysis of fit agree or disagree with the numerical analysis of fit?
Explain your answer.
10. If your graphical and numerical analysis of fit does not agree, find a better model for the
raw data. Explain why you chose that particular model.
11. Describe the data transformation used to linearize the data.
12. Write the linear regression for the transformed data.
13. Draw the residual plot for the transformed data.
14. What does the residual plot for the transformed data tell you about the raw data?
Blackline Masters, Advanced Math – Functions and Statistics
Louisiana Comprehensive Curriculum, Revised 2008
Page 126