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INTRODUCTION TO TRANSFORMATIONS Objectives: Identify Parent Functions Recognize Types of Transformations

Introduction transformations

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Page 1: Introduction transformations

INTRODUCTION TO TRANSFORMATIONS

Objectives: Identify Parent FunctionsRecognize Types of Transformations

Page 2: Introduction transformations

PARENT FUNCTIONS

Parent Function- A function that generates a family of functions.

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COMMON TYPES OF PARENT FUNCTIONS

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More Parent Function Types

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Even More Parent Functions

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TRANSFORMATIONS

Transformations- A change in the position and/or size of a figure or graph.

A "transformation” of a parent function preserves the parent function’s structure.There are 3 types of transformations:

1) Translation

2) Reflection 3) Stretch

There are 3 types of transformations:

1) Translation

2) Reflection 3) Stretch

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TRANSLATION

Translation- A transformation that moves every point on a figure a given distance in a given direction.

"Translation" simply means Shifts … without rotating, stretching or anything else, just shifts.

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REFLECTIONSREFLECTIONS Reflections- A transformation creating a

mirror image of a figure or graph on the opposite side of a line

Every point is the same distance from the central (mirror) line ... and ...The reflection has the same size as the original image

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Stretch

Stretch- a transformation in which the size of a figure or graph changes, but the shape of the figure or graph stays the same.

Stretch

Stretch in

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Transforming Parent Functions

Sketch the graph of a f(x) = √x parent function.

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Translation of Parent Function

Sketch a vertical translation

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Now sketch a horizontal translation.

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Reflection of Parent Function Sketch the parent function of a quadratic.

Sketch a vertical refection of the parent functionPossible Example:What is the line of reflection?