Chapter 1.3: Shifting, Reflecting, and Stretching Graphs

Transformations are the structual changes a function undergoes (on a graph) when a certain operation is done to the functions equation.

In this chapter we refer to the following common functions when learning about transformations.


Constant Function

Identity Function

Absolute Value Function

Square Root Function

Quadratic Function

Cubic Function

The types of transformations we have learned are Vertical Shifts, Horizontal Shifts, Vertical Stretch and Compress, Horizontal Stretch and Compress,  Reflections about the x-axis, and Reflections about the y-axis. For these examples I will use the absolute value graphs but these transformations can be applied to any parent function.

1. Vertical Shift

Parent: 

Transformations:

Green:

Blue:

2. Horizontal Shift

Parent: 

Transformations:

Blue:

Green:

REMEMBER THAT IN VERTICAL SHIFT IF THE VALUE IS NEGATIVE MOVE LEFT AND IF VALUE IS POSITIVE MOVE RIGHT.

3. Vertical Stretch and Compress

Parent: 

Transformations:

Blue:

Green:

X INTERCEPTS DO NOT MOVE

4. Horizontal Stretch

Parent: 

Transformations:

Blue:

Green:

Y VALUES OF RELATIVE MAXIMUM AND MINIMUM DO NOT CHANGE.

5. Reflection About X-Axis

Parent:

Transformation:

6. Reflection About Y-Axis

Parent=Red

Transformation=Green