Absolute Value Function Transformations

Select the correct set of transformations.

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

• Horizontal translation left 4 units

  Vertical shrink by a factor of 3 units

  Vertical translation down 2 units

• Horizontal translation right 4 units

  Vertical shrink by a factor of 3 units

  Vertical translation down 2 units

• Horizontal translation left 4 units

  Vertical shrink by a factor of 3 units

  Vertical translation up 2 units

• Horizontal translation left 4 units

  Vertical stretch by a factor of 3 units

  Vertical translation down 2 units

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?

• y = 4|-x| - 3

• y = -1/4|x| + 3

• y = 1/4|-x| - 3

• y = 1/4|-x| + 3

Determine if the translation is a vertical, horizontal, reflection, or dilation

• Horizontal

• Dilation

• Vertical

• Reflection

What is the equation of the graph below?

• f(x) = I x + 2 I 

• f(x) = I x + 2 I +2

• f(x) = I x - 2 I +2

• f(x) = I x - 2 I 

The function g can be thought of as a translation (shifted) version of f(x)=|x|. Write an equation for g(x).

g(x)=|x​ (a)   |​ (b)  

• +6

• -2

• -6

• 2

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

• reflection across x-axis

• vertical stretch

• vertical compression

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

Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units

• 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.

1) ​ (a)  

2)​ ​​ (b)  

• parent function

• shift up

• shift down

• shift right

• shift left

• reflection across x-axis

• vertical stretch

• vertical compression

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