Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the NWP Learning Commons in March 2021. The graphs are generated using Desmos. This work is licensed under a Creative Commons BY 4.0 International License.
and shift the graph 4 units upward: 
and shift it 6 units to the right:
and the function after transformation is 
. The constant number in the transformation is 
which means that it stretches the original function along the x axis.
and the constant coefficient is 
which stretches the graph in the y direction.
and we have the following transformations:
and we have the following transformations:
As the transformations are combined, a graph can be transformed point by point for simpler graphs. For the transformation of the following form, the individual points of the graph can be transformed accordingly
In this example, take the graph above and apply the following transformations
*Equations will be replaced to match above at a later date*
This final form of the transformation written out in terms of initial x and y values to the transformed x and y values is as follows with the below graph showing the results of the transformation of each point
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|---|---|---|---|
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-3 |
0 |
2 |
-1 |
|
0 |
3 |
3 |
5 |
|
3 |
-1 |
4 |
-3 |
|
6 |
2 |
5 |
3 |
