1.12 Absolute Value Transformations

Describe the transformation of the equation below from the parent function of y = IxI

y = I x + 2 I - 5

• Left 2 up 5

• Right 2 up 5

• Left 2 down 5

• Right 2 down 5

Which of the following describes the horizontal and vertical translations of the following functions:

f(x) = |x + 4| - 9

• Left 4

  up 9

• Left 4

  Down 9

• Right 4

  up 9

• Right 4

  Down 9

Describe the transformation from the Absolute Value Parent Function.

• vertical stretch 1/5, shifts up 4 units

• vertical stretch 1/5, shifts down 4 units

• vertical compression 1/5, shifts down 4 units

• vertical compression 1/5, shifts up 4 units

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

• y=6|x|-2/5

• y=2/5|x|+6

• y=2/5|x+6|

• y=2/5|x-6|

Write the equation for a graph that shifts down 9.

• y=|x|-9
• y=|x-9|
• y=-9|x|
• y=|x|+9

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

y = -2 I x - 3 I + 1

• reflected over x axis, stretched by 2, right 3, up 1

• reflected over x axis, stretched by 2, left 3 up 1

• reflected over x axis, shrunk by 2, right 3, up 1

• reflected over the x axis, shrunk by 2, left 3, up 1

Write an absolute value function given the following transformations:

Reflection across the x-axis

Vertical shift left 4 units

Horizontal shift down 7 units

• y = -|x + 4| - 7

• y = |x - 4| - 7

• y = -|x - 4| - 7

• y = -|x - 4| + 7

Describe the transformations from the parent graph to f(x) = -3∣x + 5∣ - 7

• Down 7, Left 5, Stretch by 3, reflect x-axis

• Up 7, Right 5, Stretch by 3, reflect x-axis

• Down 7, Left 5, Compress by 3, reflect x-axis

• Up 7, Right 5, Compress by 3, reflect x-axis

Write an absolute value function given the following transformations:

Vertical shift left 3 units

Horizontal shift down 2 units

• y = -|x + 3| - 2

• y = |x + 3| - 2

• y = -|x - 3| - 2

• y = -|x - 3| + 2

Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units

• f(x) = |2x + 1| - 9
• f(x) = |2x - 1| - 9
• f(x) = 2|x + 1| - 9 
• f(x) = 2|x - 1| - 9