3.4: Transformations of Absolute Value Functions

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

What shifts have occurred?

• left 1, up 5
• left 1, down 5
• right 1, down 5
• right 1, up 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 by 1/5, shifts up 4 units

• Vertical stretch by 1/5, shifts down 4 units

• Vertical compression by 1/5, shifts up 4 units

• Vertical compression by 1/5, shifts down 4 units

Describe the transformations of the absolute value equation.

• Reflection over the x-axis, Vertical compression by 3, shifts right 1 unit

• Reflection over the x-axis, Vertical compression by 3, shifts up 1 unit

• Reflection over the x-axis, Vertical stretch by 3, shifts right 1 unit

• Reflection over the x-axis, Vertical stretch by 3, shifts up 1 unit

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

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 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

Describe the transformation of the equation below:

y = I x + 3 I

• Left 3

• Right 3

• Up 3

• Down 3

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|