 Polynomial Functions of Higher Degree

 Use transformations to sketch graphs of polynomial functions.  Use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions.  Find and use the zeros of polynomial functions as sketching aids.  Use the Intermediate Value Theorem to help locate zeros of polynomial functions.

Characteristics of Graphs of Polynomial Functions 1. Polynomial functions are continuous. This means that the graphs of polynomial functions have no breaks, holes, or gaps. 2. The graphs of polynomial functions have only nice smooth turns and bends. There are no sharp turns, as in the graph of y = |x|.

Whether a graph of a polynomial eventually rises or falls can be determined by the function’s degree (even or odd) and by its leading coefficient, as indicated in the Leading Coefficient Test.

Sketching Graphs of Polynomial Functions 1. Apply the Leading Coefficient Test 2. Find the zeros of the polynomial 3. Plot a few additional points 4. Draw the graph