How do you determine the end behavior of a polynomial function?

To determine the end behavior of a polynomial function, examine the leading term, which is the term with the highest degree. The sign and degree of this term dictate the end behavior. For example, if the leading term is positive and has an even degree, both ends of the graph rise. If it is negative and even, both ends fall. For odd degrees, if positive, the left end falls and the right end rises; if negative, the left end rises and the right end falls.

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