Find vertical asymptotes, holes, and horizontal asymptote

**hubbabubba590** · March 7th 2012, 08:09 PM

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

**princeps** · March 7th 2012, 09:48 PM

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

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

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

**skeeter** · March 8th 2012, 03:05 AM

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

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