Parent Function Transformation

1
Parent Function Transformation

• Students will be able to find determine the
  parent function or the transformed function given
  a function or graph.

2
Parent Functions

• Similar to the way that numbers are classified
  into sets based on common characteristics,
  functions can be classified into families of
  functions.
• The parent function is the simplest function with
  the defining characteristics of the family.
• Functions in the same family are transformations
  of their parent function.

3
Parent Functions

• Here are some common parent functions

Linear Function
Quadratic Function
Square Root Function
Absolute Value Function
4
Absolute Value

• This is the graph of the parent absolute value
  function
• We will be investigating transformations of this
  parent function.

5
Function Family

• For a translation up or down, we change the
  parent function to a new function
• Here is an example of what this function would
  look like.

6
Function Family

• For a translation right or left, we change the
  parent function to a new function
• Here is an example of what this function would
  look like.

7
Function Family

• For a reflection across the x-axis, we change the
  parent function to a new function
• Here is an example of what this function would
  look like.

8
Function Family

• For a horizontal compression or a stretch, we
  change the parent function to a new function

If compression If
stretch Here are two examples of what this
function would look like.
9
Example 1
Identify the parent function for g from its
function rule. Then graph g on your calculator
and describe what transformation of the parent
function it represents.
1. g(x) x 7
linear translation up 7 units
10
Example 2
Identify the parent function for g from its
function rule. Then graph g on your calculator
and describe what transformation of the parent
function it represents.
2. g(x) x2 7
quadratic translation down 7 units