Alg2X – UNIT 2
Name__________________________________________ Period__________
If the directions state to EXPLAIN you need to string words together to
form a sentence. Deductions for not following directions.
DAY
1
TOPIC
Domain, Range, Relations vs. Functions,
Vertical Line Test (p. 48 #21, 31-37 if time)
2
ASSIGNMENT
1.6 pp. 47-48 #1-29 ODD, 31-33 (skip
5,11,21) 44, 46
Function notation,
independent/dependentVariables, Graphing
Functions, Word Problems
(p. 55 #21; if time go over graph for #s 3337)
More of Days 1 and 2
1.7 pp. 54-55 #1-37 odd (skip 11,19,21,
29, 31) 50-53
TBD
6
Review (10-15 min.)
QUIZ
Intro to 5 “Parent Functions” (Constant,
Linear, Quadratic, Cubic, Square Root) and
their transformations (Using Graphing
Calculator)
Compound Inequalities
7
Absolute Value Equations
8
Absolute Value Inequalities
9
Absolute Value Functions – Graphs,
Translations, Reflections
Review
3
4
5
10
11
12
More Review
And Word Problems
TEST
WORKSHEETS in Packet
1.9 pp.70-73 #1-7, 11, 12, 17-19 (use
the table feature on calc to help)
2.8 pp.154-156 # 1-4, 14, 15, 28-36
(HW in PACKET)
2.8 pp.154-156 #5-7, 16-19, 38, 49
2.8 pp.154-156 #8-13, 36, 39, 41, 42,
55-58
2.9 pp.161-163 # 2-6, 19-24, 27-29, 33,
36
pp. 78 #36-46, 53-54, p. 169 #47-56, 58
or a worksheet
Worksheet
See page 31 of packet
Reminders:
Bring your calculator every day.
Missed Tests/Quizzes:
avoid 20% reduction; don’t forget. Manage your school work please.
Mini Quizzes are always open-note.
Work hard but try not to stress.
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Life REALLY is too short.
Date _________
Period_________
U2 D1: Domain, Range, Relations vs. Functions & V. Line Test
A _____________________is a set of pairs of input and output values. You can write them as ordered pairs.
The ___________________ of a relation is the set of all inputs, or x-coordinates of the ordered pairs.
The ____________________ of a relation is the set of all outputs, or y-coordinates of the ordered pairs.
A _______________________ is a relation in which each element of the domain is paired with exactly one
element in the range.
Look for: The same x-value, but different y-values! This means it is not a function!
Are the following relations function? State why or why not! Then state the domain and range!
a)
5,1 ,  3,5 , 8,1 ,  2, 7  ,
b)
3,1 ,  2, 4 , 3,3 , 1,0 ,
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
Mapping Diagram: Identify the domain and range. Then tell whether the relation is a function.
Input
Output
Input
Output
-3
3
-3
3
1
-2
1
1
4
1
3
4
4
-2
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
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Vertical Line test: A relation is a function if and only if no vertical line intersects the graph of the relation at
more than one point. If a vertical line passes through two or more points on the graph, then the relations is
not a function.
Using the Vertical Line Test, determine whether each relation is a function. Then state the domain & range.
f x = 3x+2
2
2
f x = x2
4
2
-2
-2
Function: _________
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
Range: ___________________
8
10
6
4
5
2
-5
5
-2
10
-4
-6
-5
-8
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
For a graph to be a function, all vertical lines must touch in only _____ spot (or not touch at all)
For the domain, scan your eyes from __________ to ___________.
For the range, scan your eyes from the ___________________ to the ___________.
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Earnings Per Hour
Name
Pay
Bob
$9
Dave
$11
Jane
$5
Sam
$15
Test Scores
Name
Score
Jim
65
Greg
91
Jorge
94
Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
Closure
Why is
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 2,1 , 3,1 a function, but  2,1 ,  2,3 is not?
Terrell
88
U2 D2: Function Notation, Indep./Dep. Variables & Graphing
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Function Notation:
y  3 x  2 can be written in a “fancy notation”  f  x   3x  2 .
f  x  is read as _________________________ and does NOT mean f times x.
“Normal Way”
Function Way
1,5
f 1  5
Simplify y  2 x  1 when x  3
f  x   2 x  1 ; find f  3
Given f  x   3x  2 and g ( x)  x 2  3 , find the following:
a) f (2)
b) g ( 3)
c)
d) g (5)
1
e) f ( )
2
f) * g ( f (3))
Find f (1), f (2), f (0) .
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f (4)
Find g (1), g (3), g(5) .
Graphing functions: Do this the same why we learned to graph lines, but just replace the f ( x) (or whatever
letter it is) with ______!
Example: f ( x)  2 x  1
Example 2: g ( x)  x
Word Problems: FUN FUN FUN!
a)
b)
c)
Directions: Explain a possible domain and range for each situation
d)
e)
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Example 3: h( x)  x  1
U2 D3: Practice from Day’s 1 & 2
Directions: Graph each function below
f (2)  _______
a)
f (0)  _______
a)
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f (2)  _______
b) f (3)  _______
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Function: _________
Function: _________
Domain: __________________
Domain: __________________
Range: ___________________
Range: ___________________
Directions: For each graph below, determine it is a function (what’s the vertical line test?). Then write the
domain and range. Finally, for each graph, find the output for the corresponding input. Remember, there
could be more than one!
Function: _______________
Function: _______________
Function: _______________
Domain: _______________
Domain: _______________
Domain: _______________
Range: _________________
Range: _________________
Range: _________________
f (8)  ________________
f (2)  ________________
f (4)  ________________
Function: _______________
Function: _______________
Function: _______________
Domain: _______________
Domain: _______________
Domain: _______________
Range: _________________
Range: _________________
Range: _________________
f (2)  ________________
f (1)  ________________
f (7)  ________________
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U2 D5: Intro to Parent Functions
Graph the function f ( x)  x 2 on your calculator. Sketch the graph on the axis, and fill in the table of values.
x
y
-3
-2
-1
0
1
2
3
Look at the function, g ( x)  x 2  2 . Graph this function on your calculator, sketch the graph on the axis,
and fill in the table of values.
x
y
-3
-2
-1
0
1
2
3
How is this function different from the first one?
What do you think the function g ( x)  x 2  4 looks like?
Check your guess on your calculator.
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Use your calculator to graph each of the functions below, sketch the graph on the axis, and
describe how each one is different than
1.
g ( x)  x 2  3
f ( x)  x 2 .
4.
g ( x)  ( x  5)2
This is like f ( x)  x 2 , but…
This is like f ( x)  x 2 , but…
___________________________.
___________________________.
2.
g ( x)  x 2  5
5.
g ( x)  ( x  1)2  3
This is like f ( x)  x 2 , but…
This is like f ( x)  x 2 , but…
___________________________.
___________________________.
3.
g ( x)  ( x  4)2
6.
g ( x)  ( x  2)2  5
This is like f ( x)  x 2 , but…
This is like f ( x)  x 2 , but…
___________________________.
___________________________
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The basic function that we were working with is known as a ____________________ function. The “shifts”
(________________________) that we saw will occur in other “parents” as well.
Linear
Square Root
Cubic
Quadratic
yx
y x
y  x3
y  x2
EXAMPLES
Shifts
y  x3
y  x 3
y  x3  3
y  x2  3
y  x2
y  x 2
y  x3  2
y  x2  2
“Impossible”
y  x5
y   x  5
y   x  5
“Impossible”
y  x4
y   x  4
3
3
2
y   x  4
2
Directions: Name the parent function, and then describe the translation that will occur.
1) f ( x)  x 2  1
2) f ( x)   x  2   10
3
3) f ( x)  x  1
4) f ( x)  x  7
5) f ( x)   x  3
6) f ( x)  x  8
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2
Directions: Now, word backwards. I’ll give you the translation, you write the function.
7) f ( x)  x
Translate 5 units left and 1 units down
8) f ( x)  x 2
Translate 1 unit down
9) f ( x)  x3
Translate 2 units left and 1 unit up
10) f ( x)  x
Translate 3 units down
11) f ( x)  x
Translate 6 units right
Wrap Up:
a) What is a parent function?
b) How do translations occur? Can we generalize those translations?
c) Why is math so fun?
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U2 D6: Compound Inequalities
Warmup: Solve each inequality. Do not forget the rule that we learned in the previous chapter.
a) 3x  1  11
b) 4  x  5
c) 3x  6
d) 5x  3  2
Today we are going to discuss _______________________ inequalities. Basically this is just the
combination of 2 inequalities onto one graph. There are ______ different cases to consider.
OR
 Shade both inequalities separately, but on the same graph.
AND  Shade only the _________________ of the two graphs!
Let’s combine warmup problems a) and b) with OR, and c) and d) with AND.
Practice:
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Fancy: Combining an AND statement 
Now, work _____________________. I give you the graph, you come up with the inequality.
8)
9)
10)
11)
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Closure:
1) Describe the difference between an “AND” and “OR” compound inequality
2) What is the one key you need to remember when solving inequalities?
Extension: HW Start! The problems from the book are below.
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U2 D7: Absolute Value Equations
The absolute value of a number is always ___________________. The technical definition is the
__________________ from ______.
Therefore, 2 = _____, and when x  4 that means that x  ______ or _______!
Because numbers inside the absolute value can be _______________ or negative, we must account for two
separate cases.
Example 1: x  3  8
Example 2: 2 x  4  12
Example 3: 2 x  1  6
Example 4:
Example 5: Work backwards  Answer is x  5  3
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2x  6
4
5
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U2 D8: Absolute Value Inequalities
Warmup: Solve the two compound inequalities below and then graph!
a) 3x  2  11 or 4x  12
b) 7  2x 1  3
When solving absolute value ________________________, we create compound inequalities like the ones
we saw in the warmup. There are two distinct cases that cause the two cases: ____________ & ________.
CASE #1:
abs val  #

CASE #2:
abs val  #

Note: “or equal to” is treated the same!
a) x  8  5
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b) 3 x  1  4
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Date _________
Period_________
U2 D9: Absolute Value Functions – Graphs, Translations, Refl.
In order to graph absolute value functions on your calculator, when you’re in the functions list, push the
MATH key, then the right arrow to get to the NUMber submenu. abs( is the first function on the list.
Graph the function f ( x)  x on your calculator. Sketch the graph on the axis, and fill in the table of values.
x
y
-3
-2
-1
0
1
2
Look at the function, g ( x)  x  2 . Graph this function on your
graph on the axis, and fill in the table of values.
3
x
-3
-2
-1
0
1
2
3
How is this function different from the first one?
What do you think the function g ( x)  x  4 looks like?
Check your guess on your calculator.
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calculator, sketch the
y
Use your calculator to graph each of the functions below, sketch the graph on the axis, and describe
how each one is different than f ( x)  x .
1.
4.
g ( x)  x  5
This is like f ( x)  x , but moved…
This is like f ( x)  x , but moved…
___________________________.
___________________________.
2.
g ( x)  x  5
5.
g ( x)  x  1  3
This is like f ( x)  x , but moved…
This is like f ( x)  x , but moved…
___________________________.
___________________________.
3.
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g ( x)  x  3
g ( x)  x  4
6.
g ( x)  x  2  5
This is like f ( x)  x , but moved…
This is like f ( x)  x , but moved…
___________________________.
___________________________.
In general, we can say that the function f ( x)  x  h  k is like the f ( x)  x , but
moved ________________________________________.
Another way we can say this is that it is the same shape as f ( x)  x , but with a new
vertex at _______.
There are other translations that can happen to a parent function:
1.
g ( x)   x
This is like f ( x)  x , but…
3.
g ( x)  3x  4
This is like f ( x)  x , but…
___________________________.
___________________________.
2.
g ( x)   x  3  1
This is like f ( x)  x , but…
___________________________.
___________________________.
Conclusion:
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4.
g ( x) 
1
x5
2
This is like f ( x)  x , but…
U2 D10: Unit 2 Review
Tell whether the graph is the graph of a function. Then state the Domain and
Range for each in interval notation.
1.
2.
Function? ___________
Function? ___________
Domain: ____________
Domain: ____________
Range: _____________
Range: _____________
Show all your work, and evaluate each of the following for the functions:
f ( x)  2 x  3
g ( x) 
2
x4
5
h( x )  x 2  x
3.
f (5)
6.
4.
g ( 5)
5.
h(7)
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f (1)  g (10)
7.
Consider the equation g ( x)  x  7  2 .
a) Describe how you would use the graph of f ( x)  x to graph the function g ( x)  x  7  2 . In
other words, how would you move the original graph to accurately place the new one?
b) What are the coordinates of vertex of g(x)?
8.
What is a parent function? Use examples in your answer.
Solve, and graph your solution on a number line.
9.
5 x  9  11 AND 7 x  12  61
10.
7 x  4  3 x  12 OR
11.
5 x  12  2 x  3 OR 3  5 x  17
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9 x  15
6
5
Solve each equation.
12.
4  x 10  1
13.
4 3x  4  4 x  8
14.
3x  6  12
Solve each inequality, and graph your solution on a number line.
15.
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x 3  4
16.
2 2 x  3  10  6
17.
3 5x 1  9  24
Write the equation of each absolute value function.
18.
f ( x)  __________________
Answers!
1. yes, (-2, 4], (-3, 3]
2. no, [1, infinity), (-infinity, infinity)
3. -13
4. 6
5. 56
6. -1
7. a) left 7, down 2
b) (-7, -2)
9. (4, 7]
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19.
f ( x)  __________________
10. (-infinity, -4] or [5, infinity)
11. (-5, infinity)
12. -7, 15
13. -3/2, -1
14. -2, 6
15. (-infinity, -1) or (7, infinity)
16. [1/2, 5/2]
17. (-infinity, -4/5] or [6/5,
infinity)
U2 D11: Unit 2 Review #2 with More Translations
Directions: For each function below, please name the parent function and the translation that is caused.
1) f ( x)  x 2  5
2) f ( x)   x  3  1
3
3) f ( x)  x  2
4) f ( x)  x  4
5) f ( x)   x  2 
2
Directions: Now, word backwards. I’ll give you the translation, you write the function.
6) f ( x)  x
Translate 2 units left and 5 units down
7) f ( x)  x 2
Translate 1 unit up
8) f ( x)  x3
Translate 9 units right and 1 unit down
9) f ( x)  x
Translate 7 units up
10) f ( x)  x
Translate 6 units right
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11) Directions: Use the graph of each function to evaluate
f ( x)
g ( x)
a) f  3  _________
g  6  _________
b) f  1  _________
g  4  _________
c) f  0  _________
g  0  _________
d) f  2  _________
g  1  _________
e) f  5  _________
g  0  _________
12) Directions: Write the domain and range of each graph in interval notation.
a)
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b)
c)
Date _________
Period_________
U2 D12: Unit 2 Homework After the Test
Complete these problems from the textbook. Please be sure to show your work and write the answer
in the space provided.
Pg. 81, #1
Pg. 84, #1
Answer:
Pg. 84, #2
Answer:
Pg. 171, #3
Answer:
Pg. 171, #6
Answer:
Pg. 174, #1
Answer:
Pg. 174, #7
Answer:
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Answer:
Pg. 174, #11
Answer: