Create a rational function with the following properties:

JSmith

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Sep 21, 2012
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Create a rational function with the following properties:
f(0) = 3, there is a vertical asymptote at x = 2 and
showimage

Explain your thought process.


So I know that the function will be undefined at x=2, which means the denominator will equal 0 when x=2.
 
limxf(x)=1\displaystyle \lim_{x\to\infty} f(x) = 1 means that f(x) has as a horizontal asymptote the line y=1. What does that tell you about the degrees of your polynomials and their leading coefficients?
 
limxf(x)=1\displaystyle \lim_{x\to\infty} f(x) = 1 means that f(x) has as a horizontal asymptote the line y=1. What does that tell you about the degrees of your polynomials and their leading coefficients?

So that would mean the numerator and denominator must have the same degree, and must both have leading coefficients of 1.

So... then (x-6)/(x-2) should work... Correct?
 
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So that would mean the numerator and denominator must have the same degree, and must > > both have leading coefficients of 1. < < No, but the leading coefficients of these same degreed terms must equal each other.

So... then f(x) = (x-6)/(x-2) should work... Correct?
Yes.
 
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