2.32.3 Polynomial Functions of Higher Degree. Quick Review.

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Presentation transcript:

Polynomial Functions of Higher Degree

Quick Review

Quick Review Solutions

What you’ll learn about How to use transformations to sketch graphs of Polynomial Functions How to use the “Leading Coefficient Test” to determine End Behavior of Polynomial Functions How to find and use Zeros of Polynomial Functions How to use the Intermediate Value Theorem to locate zeros … and why These 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

Cubic Functions

Quartic Function

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

Example Applying Polynomial Theory

Example Finding the Zeros of a Polynomial Function

Example Sketching the Graph of a Factored Polynomial

Intermediate Value Theorem If 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 y 0 is between f(a) and f(b), then y 0 =f(c) for some number c in [a,b].