Math Homework. Do It Faster, Learn It Better.
Leading Coefficient Test
The graph of thepolynomial function eventually rises or falls depends on the leading coefficientand thedegree of the polynomialfunction.
Case End Behavior of graphWhenis odd andis positive Graph falls to the left and rises to the right Whenis odd andis negative Graph rises to the left and falls to the right Whenis even andis positive Graph rises to the left and right Whenis even andis negative 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.