Question

How do you sketch the general shape of `f(x)=-x^3+4x^2-7` using end behavior?

Answer 1

The general shape is that of `-x^3`

Explanation:

Since the first power is odd the general shape of the graph is similar to that of `x^3`. But we also need to take into account the negative so we say that it behaves like `-x^3`.

If the power is even then it would follow the general shape of `x^2`.

This is the graph of `-x^3`
graph{-x^3 [-10, 10, -5, 5]}

And this is the graph of `f(x)=-x^3+4x^2-7`
graph{-x^3+4x^2-7 [-22.8, 22.8, -11.4, 11.4]}