# Thread: Find vertical asymptotes, holes, and horizontal asymptote

1. ## 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

2. ## Re: Find vertical asymptotes, holes, and horizontal asymptote

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

$V.A. ~\displaystyle \lim_{x \to 0}\frac{-4x^2+1}{x^2}=\frac{1}{0}=\infty \Rightarrow x=0$

3. ## Re: Find vertical asymptotes, holes, and horizontal asymptote

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