Dilations
Definition
Dilation is the compression or stretching of a function.
Vertical Dilation
When vertical dilation is applied, the graph either moves towards (compresses or is shrunk) or moves away (stretches) from the x-axis.
These conditions apply for vertical dilation.
- :: It is compressed or shrunk towards the x-axis.
- :: It is stretched away from the x-axis.
Application
With graphing technology (e.g. Desmos), input the following functions:
Notice how with that the function stretches away from the x-axis. Notice how the opposite effect occurs with .
Horizontal Dilation
When horizontal dilation is applied, the graph either moves towards (compresses or is shrunk) or moves away (stretches) from the y-axis.
These conditions apply for horizontal dilation.
Application
With graphing technology (e.g. Desmos), input the following functions:
Notice how with that the function stretches away from the x-axis. Notice how the opposite effect occurs with . (Remember that it is the reciprocal of that is being used as the scale factor, so the scale factor of is 6, and the scale factor of is .)
Tip
To dilate a function horizontally, you must multiply x by the reciprocal of k. This is because the scale factor is actually .
Comparison
Tip
These pronumerals will be utilised for 8.06 + 8.07 - Combined Transformations. is for horizontal dilation, is for vertical dilation.
| Vertical Dilation | Horizontal Dilation |
|---|---|