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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