Free Printable Absolute Value Properties

1.

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

2.

What is the range of the function?

a)

all real numbers

b)

$y\ge3$

c)

$y\le4$

d)

3 ≤ y ≤ 7

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.

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|

5.

What is the range of the absolute value function?

a)

all real numbers

b)

$y\ge3$

c)

$y\ge0$

d)

$y<0$

6.

What is the vertex of of the graph of this equation?
$y=8\left|x-3\right|+7$

a)

(3, 7)

b)

(8, 7)

c)

(-3, 7)

d)

(-3, 8)

7.

What is the vertex of the graph of this equation?
$y=-\left|x+6\right|$

a)

(-1, 6)

b)

(-6, 1)

c)

(-6, 0)

d)

(6, 0)

8.

What is the equation of this graph?

a)

y=2|x-3|+1

b)

y=2|x-1|+3

c)

y=-2|x+1|+3

d)

y=-2|x-1|+3

9.

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

10.

Describe the transformation of the equation below from the parent function of y = I x I
y = I x - 4 I

a)

Left 4

b)

Right 4

c)

Up 4

d)

Down 4

11.

Describe the transformation of the equation below:

y = I x + 3 I

a)

Left 3

b)

Right 3

c)

Up 3

d)

Down 3

12.

What is the transformation for the following equation:

y = 5|x|

a)

Vertical Compression

b)

Vertical Stretch

c)

Up 5

d)

Left 5

13.

Describe the transformation of y = f(x) for the new function
y = 1/5f(x)

a)

The graph of y = f(x) compressed horizontally by a factor of 1/5

b)

The graph of y = f(x) was stretched horizontally by a factor of 5

c)

The graph of y = f(x) was compressed vertically by a factor of 1/5

d)

The graph of y = f(x) was stretched vertically by a factor of 5

14.

Write the equation for a graph that is vertically compressed by a factor of 2/5 and shifted up 6.

a)

y=6|x|-2/5

b)

y=2/5|x|+6

c)

y=2/5|x+6|

d)

y=2/5|x-6|

15.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, vertically stretched by 2, right 3, up 3

b)

reflected over x axis, vertically stretched by 2, left 3 up 3.

c)

reflected over x axis, vertically compressed by 2, right 3, up 3

d)

reflected over the x axis, vertically compressed by 2, left 3, up 3

16.

Identify the two solutions that make the equation TRUE

Hint: separate into two equations and find values of x from point(s) intersection.

$\left|4+2x\right|-1=19$

a)

$8,\ -12$

b)

$no\ solution$

c)

$\frac{1}{5},\ -\frac{8}{5}$

17.

Find the solutions

Hint: separate into two equations and find values of x from point(s) intersection.

−2|−2r − 4| = -12

a)

{3,1}

b)

{-5,1}

c)

{-5,5}

d)

No Solution

18.

solve for r

Hint: separate into two equations and find values of x from point(s) intersection.

- |−2r − 1| = 11

a)

{-6,5}

b)

{5,-6}

c)

-6

d)

No Solution

19.

The vertex is a ___________for this graph.

a)

maximum

b)

minimum

20.

What are the coordinates of the vertex?

a)

(-6, 4)

b)

(0,6)

c)

(0, -6)

d)

(-6, 0)

21.

What is the range for this graph?

a)

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

b)

$\left(-\infty,7\right]$

c)

$\left(7,\infty\right)$

d)

$\left[7,\infty\right)$

22.

What is the vertex of the following function?
y= 3/2 |x+3|-3

a)

(-3,-3)

b)

(3,-3)

c)

(3/2,3)

d)

(-3,3/2)

23.

What is the domain of the graph?

a)

[1,∞)

b)

(-∞,1]

c)

(-∞,∞)

d)

[-∞,∞]

24.

What is the axis of symmetry?

a)

y=5

b)

x=-3

c)

x=3

d)

y=-3

25.

What is the axis of symmetry?

a)

x=2

b)

y=2

c)

x=-3

d)

y=-3

26.

Identify the y-intercept

a)

(-1, 0)

b)

(0,-1)

c)

-1

27.

What is the axis of symmetry?

a)

x=0

b)

y=0

c)

x=-3

d)

y=-3

28.

What is the axis of symmetry?

a)

x=3

b)

y=3

c)

x=1

d)

y=1

29.

Determine the Domain of the function.

a)

$\left(3,\infty\right)$

b)

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

c)

x<3

d)

All Real Numbers

30.

Determine the Range of the functio

a)

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

b)

$y\ge2$

c)

$y\le2$

d)

$y\ge3$

31.

Choose the correct description for the transformation
$y\ =\ 3\left|x\right|$

a)

Vertical Stretch by a factor of 3

b)

Vertical Shrink by a factor of 3

c)

Vertical Compression by a factor of 1/3

d)

Vertical Compression by a factor of 1/3

32.

Choose the equation that matches the transformation:

--Reflection over the x-axis

a)

$y=-|x|$

b)

$y=|-x|$

c)

$y=\frac{1}{2}|x|$

d)

$y=2|x|$

33.

Describe the transformations of the absolute value equation.

a)

Reflects over x-axis, vertical compression by a factor of 3, right 1

b)

Reflects over x-axis, vertical compression by a factor of 3, up 1

c)

Reflects over x-axis, vertical stretch by a factor of 3, right 1

d)

Reflects over x-axis, vertical stretch by a factor of 3, up 1

Absolute Value Properties

Total questions: 33

Worksheet time: 2hrs 34mins

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