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4.3 Graphs of Polynomial Functions

# 4.3 Graphs of Polynomial Functions - Graphs of Polynomial...

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Unformatted text preview: Graphs of Polynomial Functions Section 4.3 End Behavior of Polynomial End Behavior of Polynomial Functions x When is large, the graph of a polynomial function closely resembles the graph of its highest degree term. When a polynomial function has odd degree, one end of its graph shoots upward and the other end downward. When a polynomial function has even degree, both ends of its graph shoot upward or both ends shoot downward. Leading coefficient Test Even degree an> 0 an< 0 Odd Degree an> 0 an< 0 Intercepts Intercepts The graph of a polynomial function of degree n has one y­intercept, which is equal to the constant term. has at most n x­intercepts. Multiplicity and Graphs Multiplicity and Graphs Let c be a zero of multiplicity k of a polynomial f. If k is odd, the graph of f crosses the x­ axis at c. If k is even, the graph of f touches, but does not cross, the x­axis at c. Local Extrema, Inflection Points Local Extrema, Inflection Points A polynomial function of degree n has at most n – 1 local extrema. The graph of a polynomial function of degree n, with n > 2, has at most n – 2 points of inflection. The graph of a polynomial function of odd degree has at least one point of inflection. Joke Time Joke Time What’s big, gray, and wears glass slippers? Cinderellaphant How do you prove that girls are evil? 1. 2. 3. 4. 5. 6. 7. (Submitted by Nick Collins) Girls require time & money. Girls = time x money We all know that time is money. time=money Girls = money x money (substitution) Girls = (money)2 (substitution) Money = square root of evil Girls = ( )2 (substitution) evil Girls = Evil (substitution) ...
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