## Calculus with Applications (10th Edition)

Properties of Polynomial Functions 1. A polynomial function of degree $n$ can have at most $n-1$ turning points. Conversely, if the graph of a polynomial function has $n$ turning points, it must have degree at least $n+1$. 2. In the graph of a polynomial function of even degree, both ends go up or both ends go down. For a polynomial function of odd degree, one end goes up and one end goes down. 3. If the graph goes up as $x$ becomes large, the leading coefficient must be positive. If the graph goes down as $x$ becomes large, the leading coefficient is negative. So we can determine: 1. the maximum number of turning points, 2. the end behavior of the graph (far left and far right ends), 3. which way the graph points (up or down) when x gets large.