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

reflect across the y-axis

shift left "h" units

shift down "h" units

vertical compression (wider)

shift right "k" units

vertical stretch (narrower)

shift up "k" units

shift right "h" units

shift down "k" units

reflect across the x-axis

Match the definitions and pictures with the vocabulary

• Linear Functions

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

• Absolute Value Functions

• 
• Quadratic Functions

• the simplest function of the family

• Function Family

• 
• Parent Function

• 

Match the following parent functions with their graphs and equations.

• Cubic

• 
• Exponential

• 
• Linear

• 
• Quadratic

• 
• Absolute Value

• 

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.

• Transformation

• flips a function

• Reflection

• stretches or compresses a function

• Dilation

• slides (or shifts) a function

• Translation

• turns a function about a point

• Rotation

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

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)