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

1 Answer
Jun 25, 2017

Answer:

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]}