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Sketching Polynomial Functions

Sketching Polynomial Functions 1.11 - Solution

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We want to determine the end behavior of the graph of the given polynomial function. To do so, we will pay close attention to the leading term where is the leading coefficient and is the degree of the polynomial. Let's first rewrite the given polynomial function in standard form. We can see above that the leading coefficient is and the degree is Let's now see how the leading coefficient and degree affect the end behavior of the graph of a polynomial function.

Since and is an odd number, the end behavior of the given function is up and down. We can see above that as approaches negative infinity, approaches positive infinity. As approaches positive infinity, approaches negative infinity.