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.
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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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 Winter '11
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 Calculus, polynomial function, Nick Collins

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