Introduction transformations

INTRODUCTION TO TRANSFORMATIONS

Objectives: Identify Parent FunctionsRecognize Types of Transformations

PARENT FUNCTIONS

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

COMMON TYPES OF PARENT FUNCTIONS

More Parent Function Types

Even More Parent Functions

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

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.

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

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

Transforming Parent Functions

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

Translation of Parent Function

Sketch a vertical translation

Now sketch a horizontal translation.

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?