Free Printable Absolute Value Test Review

1.

Drag and drop the transformations based on the general form of the absolute value function.

$f\left(x\right)=a\left|b\left(x-h\right)\right|+k$

Categorize the following

vertical expansion/compression

horizontal expansion/compression

horizontal translation

vertical translation

reflection over the x-axis

reflection over the y-axis

a

b

h

k

2.

Match the following description to the transformation of an absolute value:

$y=a\left|b\left(x-h\right)\right|+k$

a)

$a>1$

1.

vertical expansion

b)

$0<a<1$

2.

vertical compression

c)

$b>1$

3.

horizontal compression

d)

$0<b<1$

4.

horizontal expansion

3.

Which of the following is a graph of a vertical expansion?

a)

b)

4.

Which of the following is a graph of a horizontal expansion?

a)

b)

5.

Which of the following is a graph of a reflection over the x-axis?

a)

b)

6.

Which of the following is a graph of a reflection over the y-axis?

a)

b)

7.

Transform the parent function $y=\left|x\right|$ as described, and write the new equation.

1. Vertical translation down 4 units. (a)
2. Reflection over the x-axis. (b)
3. Horizontal expansion by $\frac{1}{4}$ . (c)
4. Horizontal translation right 4 units. (d)
5. Vertical compression by $\frac{1}{4}$ . (e)

Choose from the below words

y=\left|-x\right|

y=\left|x+4\right|

$y=\left|x\right|-4$

$y=-\left|x\right|$

$y=\left|\frac{1}{4}x\right|$

$y=\left|x-4\right|$

$y=\frac{1}{4}\left|x\right|$

8.

Select all transformations that describe the change from the parent function $y=\left|x\right|$ .

$y=-5\left|x\right|-7$

a)

vertical reflection

b)

vertical expansion

c)

down 7

d)

vertical compression

e)

horizontal compression

9.

Select all transformations that describe the change from the parent function $y=\left|x\right|$ .

$y=3\left|\frac{1}{2}\left(x+5\right)\right|-5$

a)

vertical expansion

b)

horizontal expansion

c)

horizontal shift left 5

d)

vertical shift down 5

e)

horizontal shift right 5

10.

Select all transformations that describe the change from the parent function $y=\left|x\right|$ .

$y=\left|2x+6\right|$

a)

horizontal compression

b)

horizontal shift left 3

c)

horizontal shift left 6

d)

vertical expansion

e)

horizontal expansion

11.

Select all transformations that describe the change from the parent function $y=\left|x\right|$ .

$y=\frac{1}{2}\left|\frac{1}{4}x-2\right|$

a)

vertical compression

b)

horizontal expansion

c)

horizontal shift right 8

d)

horizontal shift right 2

e)

horizontal compression

12.

Which of the following is the vertex for the following equation: $y=-\frac{1}{4}\left|2x+6\right|-7$

a)

$\left(-3,-7\right)$

b)

$\left(3,-7\right)$

c)

$\left(-6,-7\right)$

d)

$\left(6,7\right)$

13.

Given the function $f\left(x\right)=-2\left|x+1\right|$ , write a function showing g(x) as a translation of function f(x) four spaces up.

14.

Which of the following pairs of lines describes the equation $y=\left|2x+9\right|$ ?

a)

b)

c)

d)

15.

The functions f(𝑥) and g(𝑥) are graphed as shown. Which of the following represents g(𝑥) as a transformation of f(𝑥)?

There may be more than one answer.

a)

reflection over the x-axis

b)

reflection over the y-axis

c)

vertical shift up 2

d)

horizontal shift right 2

e)

vertical shift down 2

16.

$\left|ax+b\right|=c$

Solve for $x$ . Put the steps in order.

a)

set up +/- case

b)

distribute the 1/-1

c)

isolate x by +/- b

d)

isolate x by dividing by +/- a

e)

write answer in correct notation

1)

2)

3)

4)

5)

17.

Given $\left|-2x+c\ \right|\le3$ , solve the inequality for 𝑥 in terms of “c”.

a)

set up +/- cases

b)

distribute the 1/-1

c)

isolate the x by +/- c

d)

isolate the x by dividing by -2/2

e)

write answer in correct notation

1)

2)

3)

4)

5)

18.

Solve: $\left|5x-8\right|=27$

a)

$\left(7,27\right)$

b)

$\left(-\frac{19}{5},27\right)$

c)

$x=27$

d)

$x=\left\{-\frac{19}{5},7\right\}$

19.

Solve: $\left|2x-9\right|=4x-3$

a)

$\left(2,5\right)$

b)

$x=2$

c)

$x=5$

d)

$x=\left\{2,5\right\}$

20.

Solve: $\left|7x+14\right|\ge35$

a)

$\left(-\infty,-7\right]\cup\left[3,\infty\right)$

b)

$\left(-\infty,-7\right)\cup\left(3,\infty\right)$

c)

$\left(-7,3\right)$

d)

$\left[-7,3\right]$

21.

Solve: $\left|2x+5\right|<6$

a)

$\left(-\infty,-\frac{11}{2}\right]\cup\left[\frac{1}{2},\infty\right]$

b)

$\left(-\infty,-\frac{11}{2}\right)\cup\left(\frac{1}{2},\infty\right)$

c)

$\left(-\frac{11}{2},\frac{1}{2}\right)$

d)

$\left[-\frac{11}{2},\frac{1}{2}\right]$

22.

Select all of the points that are NOT in the solution set of: $\left|2x+5\right|<6$

a)

0

b)

-5.5

c)

2

d)

9

e)

-10

23.

Graph the points that are on the graph of: $y=3\left|x+2\right|-1$

when x = -4

when x = -3

when x = -2

when x = -1

when x = 0

24.

Match the following ranges that are in interval notation to their inequality notation.

a)

1.

$R:\left[3,\infty\right)$

b)

2.

$R:\ \left(-\infty,3\right)$

c)

3.

$R:\ \left(0,6\right)$

d)

4.

$R:\ \left[0,6\right]$

25.

Match each range to its corresponding absolute value function.

1. $y=\left|3x\right|$ Range: (a)

2. $y=-\left|x-4\right|+3$ Range: (b)

3. $y=3\left|\frac{1}{2}x+\frac{5}{2}\right|-7$ Range: (c)

Choose from the below words

$\left\{y\mid y\ge0\right\}$

$\left\{y\mid y\le3\right\}$

$\left\{y\mid y\ge-7\right\}$

26.

What is the domain of all absolute value functions (in interval notation)?

a)

$\left(-\infty,\infty\right)$

b)

$\left[-\infty,\infty\right]$

c)

$\left(0,\infty\right)$

d)

$\left[0,\infty\right)$

e)

$\left(\infty,-\infty\right)$

Absolute Value Test Review

Total questions: 26

Worksheet time: 8hrs 49mins

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