Objectives 

• Shifting

• Stretching

• Compressing

• Reflecting

Examples

• Example 1

• Example 2

• Example 3

• Example 4

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

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

Vertical Stretch

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

That is, it's as if you grabbed the upper ends of the original graph and then pulled up toward the ceiling.

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

Horizontal Stretch

We can stretch the graph horizontally (along the x-axis) by multiplying each x-coordinate ("inside the basic function") on the original graph by any number between 0 and 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 stretching the 
x coordinates involves the opposite arithmetic operation.
 

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