Subject: Re: Asymptotes of a rational function
Date: Tue, 23 Dec 1997 09:55:32 -0500
From: Alex Bogomolny
I've been hesitant whether to respond or not to your question. One the one hand, I sense wrong attitude towards your studies. On the other, I have no desire to preach the right one. Eventually I decided that it's worth an attempt.
The question you ask is treated in any Calculus text. Any, period. So, either you want to learn something and, then, do your homework and read the manual. Or else, there is no good reason to bother other people.
For a fraction like f(x) = (2x+3)/(x+1) the answer is immediate:
Vertical asymptote comes from x+1=0, i.e. x = -1. This is the point where f(x) is undefined.
Horizontal asymptote comes as the ratio of coefficients (by x) in the numerator and denominator of f: 2/1. So y = 2 is the only horizontal asymptote. It's the limit towards f goes as x approaches either plus or minus infinity.
Please think of it.