Graphical Behavior

End Behavior

Example 1

Which of the following could be the graph of a polynomial whose leading term is "-3x4"?

Degree_ex1



Step 1. Consider the degree.

The exponent says that this is a 4th degree polynomial, so the graph will behave roughly like a quadratic (up on both ends or down on both ends).

Step 2. Consider the leading coefficient.

Since the sign on the leading coefficient is negative, the graph will be down on both ends.

Step 3. Pick a graph.

Based on end behavior, graph B is correct.