# 2.32.3 Polynomial Functions of Higher Degree. Quick Review

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2.3Polynomial Functions of Higher Degree

Quick Review

Quick Review Solutions

What youll learn aboutHow to use transformations to sketch graphs of Polynomial FunctionsHow to use the Leading Coefficient Test to determine End Behavior of Polynomial FunctionsHow to find and use Zeros of Polynomial FunctionsHow to use the Intermediate Value Theorem to locate zeros and whyThese topics are important in modeling various aspects of nature and can be used to provide approximations to more complicated functions.

Example Graphing Transformations of Monomial Functions

Example Graphing Transformations of Monomial Functions

Cubic Functions

Quartic Function

Local Extrema and Zeros of Polynomial FunctionsA polynomial function of degree n has at most n 1 local extrema and at most n zeros.

Example Applying Polynomial Theory

Example Applying Polynomial Theory

Example Finding the Zeros of a Polynomial Function

Example Finding the Zeros of a Polynomial Function

Example Sketching the Graph of a Factored Polynomial

Example Sketching the Graph of a Factored Polynomial

Intermediate Value TheoremIf a and b are real numbers with a < b and if f is continuous on the interval [a,b], then f takes on every value between f(a) and f(b). In other words, if y0 is between f(a) and f(b), then y0=f(c) for some number c in [a,b].

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