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Math Help - vertical asymptotes

  1. #1
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    vertical asymptotes

    is \frac{1}{x^2} a vertical asymptote? Part of the definition is that the fraction must be a rational function, which means a function that can be expressed as a ratio of two polynomials. \frac{1}{x^2} cannot be expressed as a ratio of two polynomials as far as I can tell. So, am I correct that it is not a vertical asymptote?

    What is the most efficient way to identify a vertical asymptote?
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  2. #2
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    I don't think you understand what a vertical asymptote is ...

    vertical asymptotes are vertical lines with equations of the form x = k where k is a constant.

    the line x = 0 is the vertical asymptote of the function y = \frac{1}{x^2}

    go here for a lesson ...

    Vertical Asymptotes
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  3. #3
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    1 is not a polynomial

    Thanks, I read that and it says, "Vertical asymptotes correspond to the zeroes of the denominator of a rational function." 1 is not a polynomial, so how can the function be a vertical asypmptote? That is, I get that analytics of it, and I know zero in the demoninator is what we're looking for. But I don't see how the function is a rational function, I want to be able to identify rational functions.
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  4. #4
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    o.k., but understand that vertical asymptotes also exist in functions that your definition would not call "rational".
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