math sec 4.6 rw

The most general representation of a rational

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Unformatted text preview: of a rational function. The most general representation of a rational function is: a n x n + a n −1 x n −1 + a n − 2 x n − 2 + ... + a1 x + a 0 f ( x) = bm x m + bm −1 x m −1 + bm − 2 x m − 2 + ... + b1 x + b0 *Look at the degree of the polynomial Table of 3 cases…. 1. degree > numerator = no horizontal asymptotes 2. degree in numerator = degree in denominator results in 1 horizontal asymptote ex. 5x - 1 / x + 4 y=5/1= horizontal asymptote at 5 3. degree of the denominator > degree of the numerator results in the horizontal asymptote at y = 0 Ex 3. Find the horizontal asymptotes for 5x4 − 3x2 + 2 x + 1 f ( x) = 7x2 +1 3x2 − 2 x − 5 g ( x) = 2 Ex 4. x − x − 12 *None y=3 5x2 − 4x + 2 h( x) = Ex 5. 17 x 5 + 4 x 3 − x − 1 y=0 Inclined Asymptotes We will look at rational functions where the degree of t...
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This document was uploaded on 11/13/2012.

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