This document introduces transformations of parent functions including translation, reflection, and stretch. It defines each type of transformation and provides examples of how they affect the graph of a parent function. Translation moves every point a given distance in a direction without changing size or shape. Reflection creates a mirror image across a central line, with points the same distance from the line of reflection. Stretch changes only the size while maintaining the same shape.

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

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

3. COMMON TYPES OF PARENT FUNCTIONS

4. More Parent Function Types

5. Even More Parent Functions

6. 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: Translation Reflection Stretch

7. 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.     

8. REFLECTIONS 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

9. 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

10. Transforming Parent Functions Sketch the graph of a f(x) = √x parent function.

11. Translation of Parent Function Sketch a vertical translation  

12. Now sketch a horizontal translation.  

13. Reflection of Parent Function Sketch the parent function of a quadratic. Sketch a vertical refection of the parent function Possible Example: What is the line of reflection?