Question

Given `f(-3x)`, how do you describe the transformation?

Answer 1

The transformation would be reflected on the y-axis and horizontally compressed by `-(1/3)`.

Explanation:

This is because since the original function is `f(x)` and the transformation is `f(-3x)`, the difference is the `-3` in the brackets, which gives you two transformations to do: the reflection and the scaling.

• The negative sign indicates that there is a reflection, and since it's inside the brackets, `[f(-3x)]`, it will be reflected on the `y`-axis.

• The scaling of `-3` tells us that it will be a horizontal compression of `-(1/3)`, because when finding out your x values to plot and point on the graph for your transformed function (also called image), `x'=x/b`, thus the `-3` ends up at the bottom and compresses the function.

`x'=x/b`

• `x'` is the `x` of the function for the image
• `b` is the variable in front of the `x` within the brackets, in this case, it would be the `-3`.