Q:

# What is the end behavior of polynomial functions?

A:

Even and odd polynomials have different end behaviors on their graphs. Whether the leading term is positive or negative also affects the polynomial’s end behavior. Polynomials have different graphical representations based on their degree; the degree of a polynomial is the exponent to which the leading term is raised.

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Even-degree polynomials behave like quadratics, while odd-degree polynomials behave like cubic graphs. If an even-degree polynomial has a positive leading coefficient, the two ends of the graph point upward. If an even-degree polynomial has a negative leading coefficient, the two ends of the graph point downward. If an odd-degree polynomial is positive, the left end points down and the right end points up. If an odd-degree polynomial has a positive leading coefficient, the left end points up and the right end points down.

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