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Math Help - Find vertical asymptotes, holes, and horizontal asymptote

  1. #1
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    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
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  2. #2
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    Re: Find vertical asymptotes, holes, and horizontal asymptote

    Quote Originally Posted by hubbabubba590 View Post
    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
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  3. #3
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    Re: Find vertical asymptotes, holes, and horizontal asymptote

    Quote Originally Posted by hubbabubba590 View Post
    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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