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)=(-4x^{2}+1)/(x^{2})

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

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)=(-4x^{2}+1)/(x^{2})

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

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

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

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