Algebra and Trigonometry, 5th Edition

4.2 Graphing Polynomial Functions

• Graph polynomial functions.

• Use the intermediate value theorem to determine whether a function has a real zero between two given real numbers.

Graphing Polynomial Functions

In addition to using the leading-term test and finding the zeros of the function, it is helpful to consider the following facts when graphing a polynomial function.

If $P(x)$ is a polynomial function of degree n, the graph of the function has:

• at most n real zeros, and thus at most n x-intercepts;

• at most $n-1$ turning points.

(Turning points on a graph, also called relative maxima and minima, occur when the function changes from decreasing to increasing or from increasing to decreasing.)

Example 1

Graph the polynomial function $h(x)=$