Transformations of the Absolute Value Function

Describe the transformation from the Absolute Value Parent Function.

• Shift up 4 units

• Shift down 4 units

• Shift left 4 units

• Shift right 4 units

Does the following shift up or shift down from the parent function y = |x|?

• Shift up 8

• Shift down 8

• Shift right 8

• Shift left 8

What is the equation of the graph below?

• f(x) = I x + 2 I

• f(x) = 2 I x I

• f(x) = I x I +2

• f(x) = I x - 2 I

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

• Left 4

• Right 4

• Up 4

• Down 4

State the RANGE of the absolute value function given the following transformations:

• y = -|x - 2| - 7

• y = |x + 2| + 7 

• y = |x - 2| - 7 

• y = -|x - 2| + 7

For each circled number in the picture, use the drop-down option below to select the transformation it causes to the graph.

• parent function

• shift up

• shift down

• shift right

• shift left

• vertical reflection

• vertical stretch

• vertical compression

Match the descriptions to the graphs.

a

b

i

j

g

f

d

h

e

c

Horizontal stretch

Vertical compression

Horizontal compression

Vertical stretch

Negative Vertical shift

Negative Horizontal shift

Positive Vertical shift

Positive Horizontal shift

Vertical Reflection

Horizontal Reflection

y=|x−3|−1

• A

• B

• C

• D

Describe the transformations of the absolute value equation.

• Flips to A shape, compresses wider, shifts right 1 unit

• Flips to A shape, compresses wider, shifts up 1 unit

• Flips to A shape, stretches more narrow, shifts right 1 unit

• Flips to A shape, stretches more narrow, shifts up 1 unit

Which graph matches the function:
y = -2|x - 3| + 5

• A

• B

• C

• D