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

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FHS Functions 2 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. Parent Functions

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

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

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FHS Functions 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.

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FHS Functions 6 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. Function Family

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FHS Functions 7 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. Function Family

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

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FHS Functions 9 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 Example 1

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FHS Functions 10 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 Example 2

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