2nd Hour Honors Pre-Calculus Winter 2013: Chapter 1.3

Lesson 1.3- Shifting, Reflecting, and Stretching Graphs!

Graphs of Common Functions:

The six most commonly used functions in algebra are as follows:

Constant:

2) Identity: This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

3) Absolute Value: This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

4) Square Root: This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

5) Quadratic: This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

6) Cubic:

Rigid Transformations:

Rigid Transformation- type of graph transformation that does not alter the basic shape of the graph in anyway, leaving the basic shape unchanged.

Vertical and Horizontal Shifts:

The first common type of graph transformations are shifts. Shifts are rigid transformations.

Depending on the placement of a number will determine if it shifts the graph vertically or horizontally and its sign will determine which direction it will go.

If c is a positive real number than...

the graph is shifted c units upward

the graph is shifted c units down

the graph is shifted c units right

the graph is shifted c units left *Note: when c is inside parenthesis it shifts graphs in the opposite direction that what would be assumed.

Reflecting Graphs:

the second common type of graph transformations are reflections. Reflections, like shifts, are also rigid transformations

When a negative sign is present in front of x or f(x), the graph will reflect over the opposite axis. Therefore...

represents a reflection in the x-axis

represents a reflection in the y-axis

Nonrigid Transformations-

Vertical Stretches and Compresses

Because vertical stretches and compresses are nonrigid transformations, they cause distortions or changes in the shape of the original graph. Vertical stretches and compresses only appear as the value in front of f(x).