Objectives 

• Shifting

• Stretching

• Compressing

• Reflecting

Examples

• Example 1

• Example 2

• Example 3

• Example 4

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

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

Vertical Shifts:

The main idea here is to change only the y-coordinates of the points on the basic graph (using addition or subtraction "outside the basic function") while leaving the x-coordinates unchanged. 

This will cause the original graph to "slide" up or down along the y-axis.

In particular, 

• adding a positive number to the y-values ("outside the basic function") shifts the graph up

• adding a negative number to the y-values shifts the graph down.

If we only change the x-coordinates of the points (using addition or subtraction "inside the basic function") on the basic graph, while leaving the y-coordinates unchanged, the original graph will slide along the x-axis. 

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

Namely, 

• adding a positive number to each x-coordinate ("inside the basic function") causes the original graph to the shift to the left. 

• adding a negative number to the x-coordinates causes the original graph to the shift to the right. 

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

Once again, the new graph retains the original basic shape.