I'm trying to describe how the graph is related to the parent function.

Question

The parent function is x^3

and the problem is:

y=-(0.8x)^3

I know its a reflection over the x-axis, but what is the formula for how much it expands or shrinks?

Like on another problem it's

y=|x|

and y= |0.2x|

The answer is that it expands by 5, but I'm not exactly sure how to get it.

Thanks.

Answer 1

-(0.8x)^3 is stretching in the x-axis by a factor of (1/0.8) and as you noted, a reflection about the x-axis.

When ever the function f(x) is mapped to another by f(kx), it is stretching or contracting by a factor of (1/k). (1/k)>1 is a stretching, and (1/k)<1 is contracting.

Answer 2

The stretching factor (1/k) applies to the x-direction only.