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Math Help - Asymptotes

  1. #1
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    Exclamation Asymptotes

    Why do the asymptotes of y = x^2 + 1/x include y=x^2 and y=1/x?
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    Why do the asymptotes of y = x^2 + 1/x include y=x^2 and y=1/x?
    x = 0 is a vertical asymptote. It's the line through the value of x that makes the function undefined.

    y = x^2 is an oblique asymptote. It's the curve that the function approaches as x --> +oo and x --> -oo. Note: Horizontal asymptotes are a special case of oblique asymptote.
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  3. #3
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    Exclamation

    hmmmm so there is no asymptote y = 1/x (because the answer to the sheet I'm doing has the graph with that as an asymptote too ??? - the curves seem to be running beside it)

    Please help?!?
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  4. #4
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    Quote Originally Posted by xwrathbringerx View Post
    hmmmm so there is no asymptote y = 1/x (because the answer to the sheet I'm doing has the graph with that as an asymptote too ??? - the curves seem to be running beside it)

    Please help?!?
    The graph only 'runs beside' y = 1/x when both are approaching the y-axis, that is, the vertical asymptote x = 0.
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