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Absolute Value Test Review

Total questions: 62

Worksheet time: 1hrs 3mins

Name
Class
Date
1.
What is the vertex of the absolute value function?
a)
(4, 0)
b)
(0, 4)
c)
(-infinity, infinity)
d)
[4, infinity)
2.
Describe the transformation from the Absolute Value Parent Function.
a)
Shift up 4 units
b)
Shift down 4 units
c)
Shift left 4 units
d)
Shift right 4 units
3.
What is the equation of the absolute value function?
a)
f(x)= |x+4|
b)
f(x)= |x-4|
c)
f(x)= |x| + 4
d)
f(x)= |x| - 4
4.
Which function is graphed?
a)
f(x) = 2|x - 5|
b)
f(x) = |x - 5|
c)
f(x) = |x - 5| + 5
d)
f(x) = |x| + 5
5.
Which function is graphed?
a)
f(x) = 2|x + 2| -4
b)
f(x) = 2|x - 4| + 2
c)
f(x) = |x + 2| - 4
d)
f(x) = -2|x - 4|
6.

y=|x+1|−4

a)

A

b)

B

c)

C

d)

D

7.
Describe the movements.
y=|x+2|+2
a)
Left 2, Up 2
b)
Right 2, Up 2
c)
Left 2, Down 2
d)
Right 2, Down 2
8.
Which function is graphed?
a)
f(x) = 2|x + 2| -4
b)
f(x) = 2|x - 4| + 2
c)
f(x) = |x + 2| - 4
d)
f(x) = -2|x - 4|
9.

Choose the correct equation for the graph.

a)

y=∣x+3∣−4y=\left|x+3\right|-4

b)

y=∣x−3∣−4y=\left|x-3\right|-4

c)

y=∣x+3∣+4y=\left|x+3\right|+4

d)

y=∣x−3∣+4y=\left|x-3\right|+4

10.

Choose the correct equation for the graph.

a)

 y=∣x+2∣y=\left|x+2\right|

b)

y=∣x−2∣y=\left|x-2\right|

c)

y=∣x∣+2y=\left|x\right|+2

d)

y=∣x∣−2y=\left|x\right|-2

11.
What type of function is shown?
a)
linear
b)
quadratic
c)
square root
d)
absolute value
12.
Name the parent function. 
a)
constant
b)
square root
c)
linear
d)
absolute value
13.
What is the vertex of the following function?
y= 4|x|+1
a)
(0,1)
b)
(4,1)
c)
(-4,1)
d)
(4,-1)
14.

What is the vertex of the following function?

y= -2|x+10|+3

a)

(10,3)

b)

(-10,3)

c)

(-10,-3)

d)

(10,-3)

15.

What is the line of symmetry of the following function?

y= -4|x+2|+5

a)

x=-4

b)

x=2

c)

x=-2

d)

x=5

16.

What is the line of symmetry of the following function?

y= -2|x+10|+3

a)

x=-2

b)

x=10

c)

x=3

d)

x=-10

17.
Determine the transformation
a)
down 2
b)
flip, down 2
c)
flip, left 2
d)
left 2
18.
Describe each transformation
a)
stretch by factor of 1/4, right 3, down 1
b)
stretch by factor of 1/4, right 3, up 1
c)
stretch by factor of 1/4, left 3, down 1
d)
stretch by factor of 1/4, left 3, up 1
19.
Determine the Domain of the function.
a)
x > 3
b)
x < 3
c)
x > -3
d)
All Reals
20.
Determine the Range of the function
a)
All Reals
b)
y > 2
c)
x > 3
d)
y < 2
21.
Determine the Range of the function
a)
y > 1
b)
y < 1
c)
y > 2
d)
y < -2
22.
What type of shape is an absolute value function?
a)
Line
b)
V
c)
U
d)
Z
23.
What is the equation of the absolute value function?
a)
f(x)= |x+4|
b)
f(x)= |x-4|
c)
f(x)= |x| + 4
d)
f(x)= |x| - 4
24.

Which function defines the graph?

a)

f(x) = |x - 4| + 3

b)

f(x) = |x - 3| + 4

c)

f(x) = |-x + 4| + 3

d)

f(x) = |x + 4| + 3

25.
What is the vertex of the absolute value function?
a)
(4, 0)
b)
(0, 4)
c)
(-infinity, infinity)
d)
[4, infinity)
26.

Which of the following transformations describes the given function?

a)

Shift the parent function to the left 3 and up 2.

b)

Shift the parent function to the right 3 and up 2.

c)

Shift the parent function to the left 3 and down 2.

d)

Shift the parent function to the right 3 and down 2.

27.
Which equation shows a function that is translated left 4 and 7 up?
a)
y = |x + 4| + 7
b)
y = (x - 4)2 + 7
c)
y = (x + 7)2 - 4
d)
y = |x + 4| - 7
28.
y = |x| - 7 makes the graph slide . . .
a)
left 7
b)
right 7
c)
up 7
d)
down 7
29.
Find the absolute value
a)
-43
b)
43
c)
0
d)
-1
30.
Solve
a)
2
b)
-2
c)
6
d)
-6
31.

What is the value of h?


f(x) = |x + 4| - 2

a)

-4

b)

4

c)

2

d)

-2

32.

What is the value of a?


f(x) = -2|x - 4| + 3

a)

-4

b)

2

c)

-2

d)

3

33.

What is the vertex of the function?


f(x) = -2 |x + 3| - 2

a)

(-3, -2)

b)

(3, -2)

c)

(3, 2)

d)

(-3, 2)

34.

Select all that apply. (May have more than one correct answer)


f(x) = |x - 6| + 2

a)

Horizontal translation right 6 units

b)

Horizontal translation left 6 units

c)

Vertical translation up 2 units

d)

Vertical translation down 2 units

35.

Select the correct set of transformations.

f(x)=13∣x+4∣−2f\left(x\right)=\frac{1}{3}\left|x+4\right|-2  

a)

Shift the parent function to the left 4, down 2, and vertically compress by a rate of 1/3

b)

Shift the parent function to the right 4, down 2, and vertically compress by a rate of 1/3.

c)

Shift the parent function to the left 4, up 2, and vertically compress by a rate of 1/3

d)

Shift the parent function to the left 4 , down 2, and vertically stretch by a factor of 3.

36.

Select the correct set of transformations.

f(x)=−10∣x−5∣+7f\left(x\right)=-10\left|x-5\right|+7  

a)

Shift the parent function to the left 5, up 7, vertically compress by a rate -10.

b)

Shift the parent function to the right 5, up 7, vertically stretch by a rate of 10, and reflect across the line y = 7.

c)

Shift the parent function to the left 5, up 7, vertically compress by a rate of 10, and reflect across the line y = 7.

d)

Shift the parent function to the right 5 , up 7, vertically stretch by a factor of 10, and reflect across the line x = 5.

37.

What is the line of symmetry for the given graph?

a)

x = -4

b)

y = -4

c)

x = 3

d)

y = 3

38.

What is the line of symmetry for the following function?

f(x)=−6∣x+2∣−9f\left(x\right)=-6\left|x+2\right|-9  

a)

x = 2

b)

x = -2

c)

x = -9

d)

y = -9

39.

Choose the description of the transformations on f(x) = ∣x∣\left|x\right|  that result in g(x):

g(x) = - ∣x∣\left|x\right|  

a)

Reflection across the x-axis

b)

Reflection across the y-axis

c)

Vertical transition down 1

d)

Horizontal transition left 1

40.
Determine the transformation 
a)
left 3, up 2
b)
right 3, up 2
c)
left 3, down 2
d)
right 3, down 2
41.
Determine the transformation
a)
down 2
b)
flip, down 2
c)
flip, left 2
d)
left 2
42.
Determine the vertex of the function
a)
(-2, 5)
b)
(-2, -5)
c)
(2, 5)
d)
(2, -5)
43.
Determine the vertex for each absolute value function
a)
(-3, -1)
b)
(-3, 1)
c)
(3, -1)
d)
(3, 1)
44.
Determine the vertex of the function.
a)
(0, -5)
b)
(0, 5)
c)
(-2, 5)
d)
(-2, -5)
45.
What type of shape is an absolute value function?
a)
Line
b)
V
c)
U
d)
Z
46.
Which function is graphed?
a)
f(x) = 2|x + 2| -4
b)
f(x) = 2|x - 4| + 2
c)
f(x) = |x + 2| - 4
d)
f(x) = -2|x - 4|
47.
Which function is graphed?
a)
f(x) = -|2x - 3| + 5
b)
f(x) = -|x + 5| - 3
c)
f(x) = -|2x + 6| + 5
d)
f(x) = -2|x + 5| - 3
48.
Which function is graphed?
a)
f(x) = 2|x - 5|
b)
f(x) = |x - 5|
c)
f(x) = |x - 5| + 5
d)
f(x) = |x| + 5
49.
What is the equation of the graph below?
a)
f(x) = I x + 2 I 
b)
f(x) = I x + 2 I +2
c)
f(x) = I x - 2 I +2
d)
f(x) = I x - 2 I 
50.
Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9
a)
Left 4
up 9
b)
Left 4
Down 9
c)
Right 4
up 9
d)
Right 4
Down 9
51.
Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units
a)
f(x) = |2x + 1| - 9
b)
f(x) = |2x - 1| - 9
c)
f(x) = 2|x + 1| - 9 
d)
f(x) = 2|x - 1| - 9
52.

Write an absolute value function given the following transformations:

Reflection across the x-axis

Horizontal shift right 2 units

Vertical shift down 7 units

a)

y = -|x + 2| - 7

b)

y = |x - 2| - 7

c)

y = -|x - 2| - 7

d)

y = -|x - 2| + 7

53.
What is the vertex of the following function?
y= -4|x+2|+5
a)
(-4,2)
b)
(-2,5)
c)
(-4,-2)
d)
(2,5)
54.
Which function shows horizontal translation and a vertical stretch?
a)
f(x) = -2|-x | 
b)
f(x) = -3|x| - 7
c)
f(x) = -|-x + 1| + 4
d)
f(x) = 5|x - 4| - 1
55.

Select the correct set of transformations.


f(x) = 1/3 |x + 4| - 2

a)

Horizontal translation left 4 units

Vertical shrink by a factor of 3 units

Vertical translation down 2 units

b)

Horizontal translation right 4 units

Vertical shrink by a factor of 3 units

Vertical translation down 2 units

c)

Horizontal translation left 4 units

Vertical shrink by a factor of 3 units

Vertical translation up 2 units

d)

Horizontal translation left 4 units

Vertical stretch by a factor of 3 units

Vertical translation down 2 units

56.
What is the equation of the graph below?
a)
f(x) = I x + 2 I 
b)
f(x) = I x + 2 I +2
c)
f(x) = I x - 2 I +2
d)
f(x) = I x - 2 I 
57.
What is the equation of the absolute value function?
a)
f(x)= 4|x+3|
b)
f(x)= 1/4 |x+3|
c)
f(x)= 1/4 |x - 3|
d)
f(x)= 4|x - 3|
58.
Which graph matches the function:
y = -2|x - 3| + 5
a)
A
b)
B
c)
C
d)
D
59.
What is the equation of the graph below? You can click the picture to zoom in!
a)
y = - | x + 2| + 4
b)
y = - | x - 2| + 4
c)
y = | x - 2 | + 4
d)
y = | x - 2| - 4
60.

What is the equation for the absolute value parent function that has been vertically compressed by a factor of 1/4, reflected over the y-axis, and has been translated up 3 units?

a)

y = 4|-x| - 3

b)

y = -1/4|x| + 3

c)

y = 1/4|-x| - 3

d)

y = 1/4|-x| + 3

61.

Describe the transformations that took the absolute value parent function to g(x) = -|1/2(x+3)|-1

a)

Reflection over the y-axis, horizontal compression by a factor of 1/2, translation left 3 units and down 1 unit

b)

Reflection over the x-axis, horizontal stretch by a factor of 2, translation left 3 units and down 1 unit

c)

Reflection over the x-axis, horizontal stretch by a factor of 1/2, translation left 3 units and down 1 unit

d)

Reflection over the y-axis, horizontal compression by a factor of 2, translation right 3 units and down 1 unit

62.

Describe the transformation from the parent absolute value function:

y=∣x∣−5y=\left|x\right|-5  

a)

Shift up 5 units

b)

Shift down 5 units

c)

Shift right 5 units

d)

Shift left 5 units

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