ss_3_3

ss_3_3 - Section 3.3 Polynomial Functions Polynomial of...

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Section 3.3 Polynomial Functions Polynomial of degree n where n is a non-negative integer and a n 6 =0: f ( x )= a n x n + a n - 1 x n - 1 + ··· + a 1 x + a 0 Example. Polynomial function: f ( x - 2 x 3 +4 x Example. Polynomial function: f ( x )=4 Example. NOT a polynomial function: f ( x x - 3 + x Example. NOT a polynomial function: f ( x x Graphs of polynomial functions are continuous (no breaks) smooth (no sharp corners) Graph of y =( x +1)( x )( x - 1)( x - 2): –2 –1 0 1 2 –2 –1 1 2 Finding a Polynomial with given Zeros: Example. Find a polynomial of degree 3, with zeros at 3, -2, 1. Solution. f ( x a ( x - 3)( x - ( - 2))( x - 1) = a ( x - 3)( x +2)( x - 1), with a 6 = 0 arbitrary. The graph of f is shown below with a =1. –12 –6 0 6 12 3 2 1 1234 y x - 3)( x x - 1) Example. Find a polynomial with zeros of 3, -2, 1 having degree 4 and with 3 a zero of multiplicity two. Solution. f ( x a ( x - 3) 2 ( x - ( - 2))( x - 1) = a ( x - 3) 2 ( x x - 1), with a 6 = 0 arbitrary. 1
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–30 –20 –10 10 –3 –1 1 3 y =( x - 3) 2 ( x +2)( x - 1) The role of multiplicity in graphing polynomials: The graphs of f ( x )= a ( x - 1)( x - 2) n ( x -
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This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

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ss_3_3 - Section 3.3 Polynomial Functions Polynomial of...

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