Parent Function Transformation Students will be able to

Parent Function Transformation Students will be able to find determine the parent function or the transformed function given a function or graph. FHS Functions

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. FHS Functions 2

Parent Functions • Here are some common parent functions: Linear Function FHS Absolute Value Functions Quadratic Function Square Root Function 3

Absolute Value This is the graph of the parent absolute value function: We will be investigating transformations of this parent function. FHS Functions 4

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. FHS Functions 5

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. FHS Functions 6

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. FHS Functions 7

Function Family For a horizontal compression or a stretch, we change the parent function to a new function: If If compression stretch Here are two examples of what this function would look like. FHS Functions 8

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 FHS Functions 9

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) = x 2 – 7 quadratic; translation down 7 units FHS Functions 10