# Find vertical asymptotes, holes, and horizontal asymptote

• Mar 7th 2012, 08:09 PM
hubbabubba590
Find vertical asymptotes, holes, and horizontal asymptote
I'm in analytic geometry, but this problem says to analyze the function algebraically. List its vertical asymptotes, holes, and horizontal asymptote:

f(x)=(-4x2+1)/(x2)

Also, I don't quite understand what an asymptote is... I would greatly appreciate it if someone could explain
• Mar 7th 2012, 09:48 PM
princeps
Re: Find vertical asymptotes, holes, and horizontal asymptote
Quote:

Originally Posted by hubbabubba590
I'm in analytic geometry, but this problem says to analyze the function algebraically. List its vertical asymptotes, holes, and horizontal asymptote:

f(x)=(-4x2+1)/(x2)

Also, I don't quite understand what an asymptote is... I would greatly appreciate it if someone could explain

$H.A. ~\displaystyle \lim_{x \to \infty}\frac{-4x^2+1}{x^2}=\displaystyle \lim_{x \to \infty} \frac{-4+1/x^2}{1}=-4 \Rightarrow y=-4$

$V.A. ~\displaystyle \lim_{x \to 0}\frac{-4x^2+1}{x^2}=\frac{1}{0}=\infty \Rightarrow x=0$
• Mar 8th 2012, 03:05 AM
skeeter
Re: Find vertical asymptotes, holes, and horizontal asymptote
Quote:

Originally Posted by hubbabubba590
Also, I don't quite understand what an asymptote is... I would greatly appreciate it if someone could explain

Graphing Rational Functions: Introduction