Name _____________________________
Period _________________
AAT
Ch. 2 Packet
Mr. DeGroh
Mrs. Grunloh
Mrs. Sokolowski
1
Chapter 2 LEARNING TARGETS
Find the domain and the range of a function or a relation.
1
2
3
4
5
#1
Know the characteristics and forms of a linear function.
#2
1
2
3
4
5
Understand function notation and how it is used to evaluate functions.
#3
1
2
3
4
5
3
4
5
4
5
Compute the slope of a line.
#4
1
2
Understand slope as a rate of change.
#5
1
2
3
Write the equation of a line in slope intercept and point-slope form.
#6
1
2
3
4
5
Graph a linear equation using multiple forms of information.
#7
1
2
3
4
5
Write the equations of lines parallel and perpendicular in slope intercept and
point-slope form.
#8
1
2
3
4
5
2
Target #1:______________________________________________________________________
Target #2:_____________________________________________________________________
Domain:________________________________________________________________________
Range:_________________________________________________________________________
Linear Function:__________________________________________________________________
Ex. 1 Given the following graphs, determine the domain and range and whether the function is linear or not
linear. State your answer in interval notation.
a.
b.
c.
Domain:
Domain:
Domain:
Range:
Range:
Range:
Linear:
Yes
No
Linear:
Yes
No
Linear:
d.
e.
f.
Domain:
Domain:
Domain:
Range:
Range:
Range:
Linear:
Yes
No
Linear:
Yes
No
Linear:
Yes
No
Yes
No
3
Target #3:_____________________________________________________________________
Function Notation:________________________________________________________________
Ex. 2 State whether each function is a linear function. Explain.
a. f (x )  2x  5
c. y 
3
x
b. h (x )  x 2  5
d. g (x ) 
x 5
Ex. 3 Find the values of the following given f (x )  x 3  3 and g (x )  0.3x 2  3x  2.7
a. f(2)
b. f(-3)
c. g(4) + 9
d. 5g(-2)
e. f(1) + g(2)
f. 7g(3) - 10
4
Target #1, 2, & 3 Homework
Given the following graphs, determine the domain and range and whether the function is linear or not linear.
State your answer in interval notation.
1.
2.
3.
Domain:
Domain:
Domain:
Range:
Range:
Range:
Linear:
Yes
No
Linear:
Yes
No
Linear:
4.
5.
6.
Domain:
Domain:
Domain:
Range:
Range:
Range:
Linear:
Yes
No
Linear:
Yes
No
Linear:
Yes
No
Yes
No
Directions: Given f (x )  3x  5 & g (x )  x 2  4x
7) f (10)
8) g (2)
9) f (1)  g (5)
10)
3 f (4)  5
5
Target #4:_____________________________________________________________________
Slope Formulas:
Ex 1: Find the slope of the line that passes through each pair of points.
a. (-1, 4) & (3, -8)
b. (5, 3), (-4, 3)
c. (-6, 4) & (-6, 2)
 1 2 5 1 

2 3 6 4
d.  ,  ,  ,
Ex 2: Find the slope of each line shown below.
a.
b.
c.
Target #5:_______________________________________________________________
Ex. 3: In 2008 a Nintendo DS lite cost $130. In 2010 it now costs $100. Find the average rate of
change.
Ex. 4: In May, Glen sent 658 text messages. Later that year in September, he sent 874 text messages.
Find the average rate of change.
6
Ex. 5: The “slope” of a road can be defined as the “rise” divided by the “run”. Use the information below to
find the slope of the two roads. Then use the information to determine which road is steeper.
a. In road A, for every 50 feet horizontally the road rises a height of 30 feet. Determine
the slope.
b. In road B, for every 50 feet horizontally the road rises a height of 10 ft. Determine the slope.
c. Which road is steeper?
Multiple Choice Practice:
1. What is the slope of the line that passes through the points (3, 5) & (-2, 6)?
A.

1
5
B. -1
11
5
C. -5
D.
C. -1
D. undefined
2. A horizontal line has a slope of
A. 0
B. 1
3. What is the slope of the line of the figure shown at the right?
A.
4
3
B.
3
4
C. 
4
3
D. 
3
4
4. For 4 hours of work you earned a $37 and for 11 hours of work you earned $101.75, find your average
rate of change.
A. $4.31
B. $9.25
C. $19.82
D. $8. 25
7
Target #4 & 5 Homework
Slope Formulas:
Find the slope of the line that passes through each pair of points.
1. (-1, 4), (3, -8)
2. (-2, 11), (5, 6)
3. (-1.5, 3.5), (4.5, 6)
5.
6.
4. (8, 2), (8, -100)
7.
8. Find the rate of change given:
Time (min)
Distance (ft)
2
12
4
24
6
36
8
48
10
60
9. In 2006 the cost of a desktop computer was $860. In 2010 a desktop computer costs $376. Find the
average rate of change.
10. After 6 days you made 11 tweets on Twitter and after 9 days you made a total of 25 tweets, find your average
rate of change between days 6 and 9.
8
Review Sheet TARGETS 1 - 5
Target #1 State the domain & range of a function.
Target #2: Know characteristics and forms of a linear function.
1-8. For the following relations or functions, find the domain and range then state whether the is linear or non-linear
by circling yes or no.
1)
Linear? Yes
No
2)
Range:____________
Range:____________
5)
Linear? Yes
4)
No
Linear? Yes
No
Domain:___________
Domain:___________
Range:____________
Range:____________
Linear? Yes
No
6)
Linear? Yes
Domain:___________
Linear? Yes
No
No
Domain:___________
Range:____________
7)
No
Domain:___________
Domain:___________
3)
Linear? Yes
Range:____________
8)
Linear? Yes
No
Domain:___________
Domain:___________
Range:____________
Range:____________
9
Target #3: Understand function notation & how it is used to evaluate functions.
If
f ( x)  x 2  3x and g ( x)  4  2 x
9) Find
If
f  3
10) Find
2 g  5
11) Find
f (7)  g  7 
h( x )   x 2  6 & f ( x )  3 x  2 x 3
12) Find h( 3)  7
13) h(2)  f ( 5)
14)
4 f  2  3
Target #4: Compute the slope of a line.
15) Find the slope between
(5,10) & (-1,-2)
16) Find the slope of the lines shown below.
a.
b.
Target #5: Understand slope as a rate of change.
17) Find the rate of change given:
Hours
Pay
3
$12.75
7
$29.75
9
$38.25
18) In 2008 Jill sent a total of2650 text messages.
In 2010 she sent 4830 messages. Find the rate of change.
13
$55.25
19) Mrs. Sokolowski bought a new Honda in 2009 for $29500. Now, in 2011 it is worth $27,205. What is the rate of
change per year?
10
Target #6_______________________________________________________________
Different Forms of Linear Equations:
1._________________________________ 2.___________________________________
Ex 1: Write an equation of the line show in the graph in slope-intercept form.
a.
b.
d.
e.
c.
f.
11
Ex 2: Write an equation in slope-intercept form for the line described.
a. slope = 
3
& passes through (5, -2)
5
b. slope =
1
& passes through (-5, -8)
3
Ex 3: Write an equation of the line passing through each pair of points.
a. (-2, 7) & (3, -3)
b. (4, -9) & (2, -4)
Ex 4: The sales of a sandwich store increased approximately linearly from $52,000 to $116,000
during the first 5 years.
a. Write an equation that models the sales, y, after x years.
b. What does the slope represent in this problem?
c. What will the sales be at the end of 12 years if the pattern continues?
12
Target #6 Homework
Write the equation of the line in slope-intercept form given the following.
1.
2.
4. slope: 3, passes through (-3, 14)
3.
5. slope: 
1
, passes through (12, -4)
4
6. slope: undefined, passes through (-6, -8)
7. (-2, -6), (4, 6)
8. (-8, -5), (-3, 10)
9. (-25, -16), (-29, 12)
10. The surface of Grand Lake is at an elevation of 648 feet. During the current drought, the water level is
dropping at a rate of 3 inches per day. If this trend continues, write an equation that gives the elevation in
feet of the surface of Grand Lake after x days.
13
Target #7:_____________________________________________________________________
Ex. 1 Given the following information, graph the lines.
a. (2, -3), (0, 4)
d. y  x
g.
2
1
x  y 1
3
4
b. m =
1
, pt(-3, -4)
3
e. 3x  8y  40
h. m= 0, pt(-4, 5)
c. m = -5, b = 1
f. y  1  2(x  3)
i. m = und, pt(3, -2)
14
Review TARGETS 6 & 7
Form
Slope-Intercept
Formula
Point-slope
Slope Formula
Target 6: Writing equations of lines in slope-intercept form.
Write an equation for the graph shown. Be sure the equation is in slope-intercept form.
1.
2.
3.
Equation:________________
Equation:_______________
Equation:______________
Write the slope-intercept form equation for each situation below.
4. slope = -4 & y-intercept = 9
6. m =
1
& (-9, 6)
3
5. Horizontal line passing through (-1,6).
7. (-3, 8) & (1, 4)
15
8. The Geek Squad charges a flat fee of $50 to come and assess your computer problem plus a $25 per hour fee to fix
the problem. A. Write a linear equation in slope intercept form to represent this situation for total cost (y) in terms of
the number of hours (x) needed to fix the computer. Use the equation to calculate the how many hours it took to fix
your computer if the cost $225.
Target 7: Graphing equations
Sketch the graph. Make sure equations are in slope-intercept form first.
9. (4, -3) with slope = 2
10. Slope = -2 & y-intercept= 5
12. (4, -5), (-3, 2)
15.
y 3
13.
16.
3x  y  5
y4
2
 x  3
3
11. Slope = undefined, point (-3,1)
14.
2 x  3 y  9
17.
1
4
y x 
3
3
16
Target #8:_____________________________________________________________________
Remember these main ideas:
1) If the ___________________ of lines are _____________________,
then the lines are _______________________________.
2) If the ___________of lines are ___________________ & __________________,
then the lines are ___________________________________.
Ex 1: Write an equation in slope-intercept form that satisfies each set of conditions.
a. passes through (4, 1) & parallel to
y  3x  5
b. passes through (-5, 7) & perpendicular to
c. passes through (4, -10) & parallel to y 
y  5 x  3
7
x3
8
5
d. passes through (-9, -3) & perpendicular to y   x  8
3
17
e. parallel to x-axis passing through (4, -3)
f. parallel to the y-axis passing through the point (-2, 3)
g. perpendicular to the line y = -3 passing through the point (5, -8)
18
Target #8 Homework
1. Find the equation of the line that passes through
(2, -4) and is perpendicular to the line y  2x  5 .
2. Find the equation of the line parallel to
3. Write the equation of the line through (3, -5)
that is parallel to a line passing through the points
(8, 4) and (12, 5).
4. Find the slope of the line that is perpendicular
to a line with the given points (8, 6) and (8, -6).
5. Determine whether these two lines are parallel,
perpendicular or neither.
6. Write the equation of the line that is
perpendicular to the x-axis and passes through
(-5, -6).
2y  3x  8

3y  2x  27
7. Write the equation of the line that is parallel to
the x-axis and passes through (1, 19).
1
y   x  7 through (6, 5).
3
8. Write two equations of lines that are
perpendicular.
Line 1:_____________________________
Line 2:_____________________________
19
Test Review ALL TARGETS 1, 2,3,4,5,6,7,8
Target 1: State Domain & Range of a function.
Target 2: Know characteristics of a linear function.
Find the domain & range. State if the function is linear or not.
1.
2.
3.
Domain:__________
Domain:_____________
Range:__________
Range:_____________
Linear: y or n
Linear: y or n
5.
4.
Domain:___________
Domain:__________
Range:___________
Range:___________
Linear: y or n
Linear: y or n
6.
Domain:__________
Domain:___________
Range:__________
Range:___________
Linear: y or n
Linear: y or n
Target 3: Use function notation to evaluate functions.
f ( x)  2 x2  x & g ( x)  3x  1 & h( x)  ( x  1)2
7. f (3)
8. g  
2
1
9. h(4)
10. f (2)  g (2)
11. h(1)  f (1)  g (1)
20
Target 4: Compute the slope of a line
Find the slope from the give information.
12. (-3, 5) & (2, -10)
13.
14. (5, -2) & (5, 0)
15.
16. Find r from the given slope & points.
m
1
points (-1, r) & (11 ,2)
3
Target 5: Understanding slope as a rate of change.
17. Emma earned $126 in 3 weeks of babysitting. After babysitting for 8 weeks she has earned $336.
Find the average rate of change.
18.
In the year 2007, GNHS had 346 in the graduating class. In 2010 the graduating class was 544. What is the
average rate of change.
Target 6: Writing equations of lines in slope-intercept form.
Write the equation of the line in slope-intercept form from the given information.
19. Slope =-4 & y-intercept =9
20. Slope = 3 passes through (-4, 1)
21. (16, -2) & (4, 4)
22.
Vertical line thru (6, -5)
21.
23.
(-8, 5) & m =
1
4
21
Target 7: Graphing equations of lines from given information.
24. 2 y  x  4
27. y  2
25. (-3, 5) with slope = -2
28.
1
1
3
y  x
4
2
4
26.
y4
1
 x  5
5
29. Slope = 
4
& y-intercept= 3
5
Target 8: Write equations of lines parallel and perpendicular to given lines.
30. Write an equation of the line parallel to y 
1
x  5 that passes through the point (-4, 1).
2
31. Write an equation of the line perpendicular to y 
1
x  5 passing through (-10, 5).
2
22
32. Write an equation of the line perpendicular to the y-axis passing through (-2,-3).
33. Write the equation of the line through (1, -7) that is parallel to a line passing through
the points (3, 4) and (-2, 9).
34. Determine if the lines are parallel, perpendicular or neither
3y  6x  9
x  2y  6
35. Write an equation of the line parallel to the y-axis passing through the point (8,-5).
36. Write 2 equations of lines that are parallel.
23