The graph of the polynomial function eventually rises or falls depends on the leading coefficient and the degree of the polynomial function.

Case End Behavior of graphWhen nis odd andais positive_{n}Graph falls to the left and rises to the right When nis odd andais negative_{n}Graph rises to the left and falls to the right When nis even andais positive_{n}Graph rises to the left and right When nis even andais negative_{n}Graph falls to the left and right

**Example: **

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function .

Solution:

Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right as shown in the figure.