Determine end behavior (long run behavior) of polynomial functions

The graphs of polynomial functions are discussed as we say that they must be both smooth and continuous with no sharp corners, cusps, gaps, or breaks. Then we look at their end behavior based on the end behavior of their leading terms. Arrow notation is used to describe this behavior as x approaches infinity and negative infinity. We then look at the possibilities for the degree of a polynomial when given a graph and the sign for its leading coefficient.