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

1 Answer
Jun 25, 2017

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]}