precalculus
posted by Chris on .
I'm trying to describe how the graph is related to the parent function.
The parent function is x^3
and the problem is:
y=(0.8x)^3
I know its a reflection over the xaxis, 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.

(0.8x)^3 is stretching in the xaxis by a factor of (1/0.8) and as you noted, a reflection about the xaxis.
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. 
The stretching factor (1/k) applies to the xdirection only.