Question

how are dilations and functions related?

Answer 1

If we dialate a function we are just changing what the graph looks like by a stretch or a compression, the function really doesn't change.  If a function before the dilation, then it is a function after the dilation.  The opposite is also true.

Answer 2

Answer:

A function is said to be dilated when it has been stretched away from an axis or compressed toward an axis. This dilation can be a vertical or a horizontal stretch.

When the given function is multiplied by any number, it will automatically dilate but at the same time, will also retain its basic shape.