Absolute Value Functions Transformations

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

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 up 1 unit

Describe the transformation that is applied to the parent function. 
f(x) = IxI -5

• Shifts left 5

• Shifts right 5

• Shifts up 5

• Shifts down 5

Does the following shift up or shift down from the parent function y = |x|?
y = |x| - 8

• Shift up

• Shift down

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 

Which function is graphed?

• f(x) = -|2x - 5| + 5

• f(x) = -|x - 3| - 3

• f(x) = -2|x + 3| + 5

• f(x) = -2|x + 5| - 3

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

• vertical reflection

• 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.

1) ​ (a)  

2) ​ (b)  

• parent function

• shift up

• shift down

• shift right

• shift left

• vertical reflection

• 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.

1) ​ (a)  

2) ​ (b)  

3)​ ​ ​ (c)  

4) ​ (d)  

• parent function

• shift up

• shift down

• shift right

• shift left

• reflection across x-axis

• vertical stretch

• vertical compression