3.5 - Rational Functions and Asymptotes

# 3.5 - Rational Functions and Asymptotes - &lt;?xml...

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<?xml version="1.0" encoding="iso-8859-1"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>3.5 - Rational Functions and Asymptotes</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> </head> <body> <h1>3.5 - Rational Functions and Asymptotes</h1> <p>A rational function is a function that can be written as the ratio of two polynomials where the denominator isn't zero.</p> <p>f(x) = p(x) / q(x)</p> <h2>Domain</h2> <p>The domain of a rational function is all real values except where the denominator, q(x) = 0.</p> <h2>Roots</h2> <p>The roots, zeros, solutions, x-intercepts (whatever you want to call them) of the rational function will be the places where p(x) = 0. That is, completely ignore the denominator. Whatever makes the numerator zero will be the roots of the rational function, just like they were the roots of the polynomial function earlier. </p> <p>If you can write it in factored form, then you can tell whether it will cross or touch the x-axis at each x-intercept by whether the multiplicity on the factor is odd or even.</p>

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## This note was uploaded on 10/18/2011 for the course MAT 1033 taught by Professor Brown during the Spring '10 term at Valencia.

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3.5 - Rational Functions and Asymptotes - &lt;?xml...

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