Question

How are the graphs `f(x)=x^3` and `g(x)=-(2x)^3` related?

Answer 1

The graph of `g(x)` can be described as a transformation of the graph of `f(x)`.

Explanation:

First, take a look at the graph of `f(x)`.
graph{x^3 [-10, 10, -5, 5]}

Now look at the graph of `g(x)`.
graph{-(2x)^3 [-10, 10, -5, 5]}

The graph of `f(x)` is horizontally shrunk by a factor of `1/2` and reflected over the `y`-axis to get the graph of `g(x)`.