Deck 9: New Functions From Old
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Deck 9: New Functions From Old
1
Select the equation whose graph is the graph of
vertically stretched by a factor of 8.
A)
B)
C)
D)

A)

B)

C)

D)


2
Select the choice which best describes the graph of . 
A) It is the graph of
shifted 8 units to the left.
B) It is the graph of
vertically stretched by a factor of 8.
C) It is the graph of
shifted 8 units down.
D) It is the graph of
vertically stretched by a factor of 8 and reflected across the x-axis.

A) It is the graph of

B) It is the graph of

C) It is the graph of

D) It is the graph of

It is the graph of
vertically stretched by a factor of 8.

3
Select the equation whose graph is the graph of
vertically stretched by a factor of
and reflected across the x-axis.
A)
B)
C)
D)


A)

B)

C)

D)


4
Select the choice which best describes the graph of
.
A) It is the graph of
shifted 2 units to the right.
B) It is the graph of
vertically stretched by a factor of 2.
C) It is the graph of
shifted 2 units up.
D) It is the graph of
vertically stretched by a factor of 2 and reflected across the x-axis.

A) It is the graph of

B) It is the graph of

C) It is the graph of

D) It is the graph of

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5
Select the equation whose graph is the graph of
shifted 6 units up.
A)
B)
C)
D)

A)

B)

C)

D)

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6
Select the choice which best describes the graph of . 
A) It is the graph of
shifted 6 units up.
B) It is the graph of
vertically stretched by a factor of 6.
C) It is the graph of
shifted 6 units to the right.
D) It is the graph of
shifted 6 units down.

A) It is the graph of

B) It is the graph of

C) It is the graph of

D) It is the graph of

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7
Select the equation whose graph is the graph of
shifted 10 units to the right.
A)
B)
C)
D)

A)

B)

C)

D)

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8
Select the choice which best describes the graph of . 
A) It is the graph of
shifted 9 units to the right.
B) It is the graph of
vertically stretched by a factor of 9.
C) It is the graph of
shifted 9 units down.
D) It is the graph of
shifted 9 units to the left.

A) It is the graph of

B) It is the graph of

C) It is the graph of

D) It is the graph of

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9
Select the equation whose graph is the graph of
reflected horizontally (across the y-axis).
A)
B)
C)
D)

A)

B)

C)

D)

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10
Select the choice which best describes the graph of . 
A) It is the graph of
reflected vertically (across the x-axis).
B) It is the graph of
shifted 1 unit to the right.
C) It is the graph of
shifted 1 unit down.
D) It is the graph of
reflected horizontally (across the y-axis).

A) It is the graph of

B) It is the graph of

C) It is the graph of

D) It is the graph of

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11
Transform the function
into a new function
by compressing
by a factor of 0.3, reflecting across the x-axis, and then shifting the result down 8 units. Find the equation of
.




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12
Transform the function
into a new function
by compressing
by a factor of 0.9 and reflecting across the x-axis, and then shifting the result up 4 units. Find the equation of
.




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13
Transform the function
into a new function
by shifting
horizontally 3 units to the left and then shifting the result down 6 units.Find the equation of
.




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14
Transform the function
into a new function
by reflecting
horizontally (across the y-axis) and then shifting the result up 3 units.
Find the equation of
.



Find the equation of

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15
Transform the function
into a new function
by shifting
horizontally 10 units to the right, reflecting the result across the x-axis, and then shifting the result down 6 units.
Find the equation of
.



Find the equation of

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16
Find the formula for
where 


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17
Find a formula for
where 


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18
Find a formula for
where 


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19
Find a formula for
where 


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20
Transform the function
into a new function
by reflecting horizontally (across the y-axis), stretching
by a factor of 7 , and then shifting the result up 9 units.
Find the equation of
.



Find the equation of

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21
Find a formula for
where 


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22
If graph A is the graph of
, which of the following will yield graph B?

A)
B)
C)
D)


A)

B)

C)

D)

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23
If graph A is the graph of
, which of the following will yield graph B?

A)
B)
C)
D)


A)

B)

C)

D)

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24
If graph A is the graph of
, which of the following will yield graph B?

A)
B)
C)
D)


A)

B)

C)

D)

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25
If graph A is the graph of
, which of the following will yield graph B?

A)
B)
C)
D)


A)

B)

C)

D)

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26
If graph A is the graph of
, which of the following will yield graph B?

A)
B)
C)
D)


A)

B)

C)

D)

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27
If graph A is the graph of
, which of the following will yield graph B?

A)
B)
C)
D)


A)

B)

C)

D)

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28
If graph A is the graph of
, which of the following will yield graph B?

A)
B)
C)
D)


A)

B)

C)

D)

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29
If graph A is the graph of
, which of the following will yield graph B?

A)
B)
C)
D)


A)

B)

C)

D)

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30
Use the graph of
below to determine which statement is true.

A)
is not symmetric
B)
is symmetric about the origin
C)
is symmetric across the y-axis
D)
is symmetric across the x-axis


A)

B)

C)

D)

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31
Determine which statement is true for . 
A)
is symmetric across the x-axis.
B)
is symmetric across the y-axis.
C)
is symmetric about the origin.
D)
is not symmetric.

A)

B)

C)

D)

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32
Determine which statement is true for . 
A)
is symmetric across the x-axis.
B)
is symmetric across the y-axis.
C)
is symmetric about the origin.
D)
is not symmetric.

A)

B)

C)

D)

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33
Determine which statement is true for . 
A)
is symmetric across the x-axis.
B)
is symmetric across the y-axis.
C)
is symmetric about the origin.
D)
is not symmetric.

A)

B)

C)

D)

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34
Determine which statement is true for 
A)
is symmetric across the x-axis.
B)
is symmetric across the y-axis.
C)
is symmetric about the origin.
D)
is not symmetric.

A)

B)

C)

D)

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35
Determine which statement is true for 
A)
is symmetric across the x-axis.
B)
is symmetric across the y-axis.
C)
is symmetric about the origin.
D)
is not symmetric.

A)

B)

C)

D)

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36
Determine which statement is true for 
A)
is symmetric across the x-axis.
B)
is symmetric across the y-axis.
C)
is symmetric about the origin.
D)
is not symmetric.

A)

B)

C)

D)

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37
Identify the function 
A) Even
B) Odd
C) Neither

A) Even
B) Odd
C) Neither
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38
Identify this graph as symmetrical about the x-axis, y-axis, or the origin.

A) X-axis
B) Origin
C) Y-axis
D) Neither

A) X-axis
B) Origin
C) Y-axis
D) Neither
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39
Given the function
, the function
is created by reflecting f(x) around the
A) origin.
B) Not a reflection
C) y-axis.
D) x-axis.


A) origin.
B) Not a reflection
C) y-axis.
D) x-axis.
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40
Evaluate
where
and 



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41
Evaluate
where
and 



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42
Evaluate
where
and 



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43
Evaluate
where
and
Write your answer as a reduced fraction.



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44
Find
where
and 



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45
Find
where
and 



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46
Find
where
and 



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47
Find
where
and 



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48
Evaluate
where
and
Give an exact answer in the form of a reduced fraction.



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49
Evaluate
where
and
Give a decimal answer. Round your answer to 2 decimal places, if necessary.



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50
Evaluate
where
and
Give an exact answer in the form of a reduced fraction.



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51
Evaluate
where
and
Give a decimal answer. Round your answer to 2 decimal places, if necessary.



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52
Evaluate
where
and
Give an exact answer in the form of a reduced fraction.



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53
Evaluate
where
and
Give a decimal answer. Round your answer to 2 decimal places, if necessary.



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54
Evaluate
where
and
Give an exact answer in the form of a reduced fraction.



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55
Evaluate
where
and
Give a decimal answer. Round your answer to 2 decimal places, if necessary.



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56
Use the table to evaluate the function :



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57
Use the table to evaluate the function :



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58
Use the table to evaluate the function
: (Round the answer to 2 decimal places if necessary.)



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59
If f(x) = 4x and g(x) = 2x, evaluate . 

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60
Use the table to create a table for the function
: (Round the answer to 2 decimal places if necessary.) 


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61
Use the table to create the table for the function :



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62
Given the functions shown in this graph, select the graph that shows . 

A)

B)

C)

D)



A)

B)

C)

D)

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63
At most how many turning points does the graph of
have?

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64
At most how many horizontal intercepts does the graph of
have?

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65
Choose the description that describes the end behavior of the graph of . 
A)
and 
B)
and 
C)
and 
D)
and 

A)


B)


C)


D)


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66
Choose the function below whose end behavior matches the description.
and 
A)
B)
C)
D)


A)

B)

C)

D)

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67
Which of the following describes the polynomial pictured?

A) It is a degree 4 polynomial with a negative leading term.
B) It is a degree 4 polynomial with a positive leading term.
C) It is a degree 3 polynomial with a negative leading term.
D) It is a degree 3 polynomial with a positive leading term.

A) It is a degree 4 polynomial with a negative leading term.
B) It is a degree 4 polynomial with a positive leading term.
C) It is a degree 3 polynomial with a negative leading term.
D) It is a degree 3 polynomial with a positive leading term.
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68
What is the minimum degree of the polynomial pictured?


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69
What is the minimum degree of the polynomial pictured?


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70
Find the horizontal intercepts of the function .
Write your answers
in ascending order . 



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71
Find the horizontal intercepts of the function .
Write your answers
in ascending order . 



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72
Find the horizontal intercepts of the function .
Write your answers
in ascending order . 



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73
Find a polynomial function with horizontal intercepts -6, 2, and 6 and vertical intercept -72.
Write your answer in standard form, .
Write your answer in standard form, .

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74
Find a polynomial function with horizontal intercepts -6, -5, -1, and 1 and vertical intercept 30.
Write your answer in standard form, .
Write your answer in standard form, .

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75
Find a polynomial function with horizontal intercepts 1, 2, 3, 4, and 7 and vertical intercept -168.
Write your answer in standard form, .
Write your answer in standard form, .

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76
Find a polynomial function with horizontal intercepts 2, 4, and 5 and vertical intercept 120.
Write your answer in factored form,
with . 
Write your answer in factored form,


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77
Find a polynomial function with horizontal intercepts -9, -8, 1, and 6 and vertical intercept -864.
Write your answer in factored form,
with . 
Write your answer in factored form,


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78
Find a polynomial function with horizontal intercepts 2, 4, 5, 6, and 9 and vertical intercept 6480.
Write your answer in factored form,
with . 
Write your answer in factored form,


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79
State the degree of the function:


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80
Evaluate the following expression for x = -3.


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