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Explore graphs of polynomial functions, coefficient tests, finding zeros, and sketching techniques. Understand continuous vs. not continuous, leading coefficients, odd and even exponents. Apply the Intermediate Value Theorem. Learn to describe end behaviors and discover polynomial functions from given zeros.
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Chapter 2: Lesson 2.2Polynomial Functions of Higher Degree This lesson is largely based on discussions of graphs in the text • Continuous vs not continuous p 124 Figure 2.6 • Smooth rounded curves vs sharp turns p 124 Figures 2.7 and 2.8 HW #15
Leading Coefficient Test Odd Exponent Lead coefficient (a) is positive then x →∞, y→∞ and x →-∞, y→-∞ Lead coefficient (a) is negative then x →∞, y→-∞ and x →-∞, y→∞ Even Exponent 1) Lead coefficient (a) is positive then x →∞, y→∞ and x →-∞, y→∞ 2) Lead coefficient (a) is negative then x →∞, y→-∞ and x →-∞, y→-∞ See page 126 Use the coefficient test to describe the end behavior of:
Finding Zeros The maximum number of turning points (transitions from increasing to decreasing or transitions from decreasing to increasing) is always 1 less than the exponent of the lead variable.
Given Zeros Find the Polynomial Function Find the polynomial function with the given real zeros or x-intercepts. #57 2, -6
