Parent Functions and Transformations of Absolute Value Functions

Complete the chart by labeling the rules with the resulting transformations

a

b

c

h

g

e

f

vertical stretch (narrower)

shift up "k" units

shift right "k" units

reflect across the y-axis

shift right "h" units

shift down "k" units

vertical compression (wider)

shift left "h" units

reflect across the x-axis

shift down "h" units

Match the definitions and pictures with the vocabulary

• Parent Function

• the simplest function of the family

• Absolute Value Functions

• 
• Quadratic Functions

• 
• Linear Functions

• a set of functions whose equations and graphs have a similar form and shape

• Function Family

• 

Match the following parent functions with their graphs and equations.

• Exponential

• 
• Quadratic

• 
• Absolute Value

• 
• Linear

• 
• Cubic

• 

Describe how the following function compares to the parent function for f(x) = |x| - 3.

​ (a)  

• shift down 3 units
• shift up 3 units
• shift left 3 units
• shift right 3 unitis
• flip over the x-axis
• flip over the y-axis
• vertical stretch by a factor of 3
• vertical compression by a factor of ⅓

Write the function to transform the parent function for f(x) = |x| when the graph is shifted left 7 units.

​ (a)  

• f(x) = |x + 7|
• f(x) = |x − 7|
• f(x) = 7|x|
• f(x) = -7|x|
• f(x) = |x| + 7
• f(x) = |x| − 7

Match the following vocabulary and definitions.

• Translation

• stretches or compresses a function

• Rotation

• slides (or shifts) a function

• Reflection

• turns a function about a point

• Dilation

• changes the position or size of a figure; can be applied to parent functions

• Transformation

• flips a function

Describe how the following function compares

to the parent function f(x) = |x|

f(x) = -|x − 4|

• shifted right 4 units

• reflected over x-axis

• shifted left 4 units

• shifted up 4 units

• shifted down 4 units

Write the new function for the transformation: Vertically stretched by a factor of 5, then translated 1 unit left.

f(x) = ​ (a)   | x​ (b)   |

• 5
• + 1
• -5
• − 1

Write the new function for the transformation:

Vertically stretched by a factor of 2, then translated 9 units down.

f(x) = ​ (a)   |x​ (b)   | ​ ​ (c)  

​

• 2
• + 0
• − 9
• -2
• + 9
• ½
• -½

Graph the function f(x) = 2|x| + 1.

Identify the vertex of the graph.

• (-1, -2)

• (0, 1)

• (1, -1)

• (0, 0)

• (1, 0)