Objectives 

• Shifting

• Stretching

• Compressing

• Reflecting

Examples

• Example 1

• Example 2

• Example 3

• Example 4

A graph may be compressed vertically along the y-axis or horizontally along the x-axis.

The type of compression depends on whether the y-coordinate or the
x-coordinate is being changed.

Vertical Compression

We can compress the graph vertically (along the y-axis) by multiplying each y-coordinate ("outside the basic function") on the original graph by any number between 0 and 1, while leaving the x coordinates unchanged.
 

The new graph retains the same basic shape as the original graph.

Horizontal Compression

We can compress the graph horizontally (along the x-axis) by multiplying each x-coordinate ("inside the basic function") on the original graph by any number greater than 1, while leaving the y coordinates unchanged.

Note! When we are changing x-values, the effect on the graph
           seems "backwards" from what it should be. 

This "backwardsness" is necessary so that the original y-coordinates will remain unchanged.

Click here for a more detailed discussion of why compressing the x coordinates involves the opposite arithmetic operation.