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Math Help - Why can't a graph...

  1. #1
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    Why can't a graph...

    ...have more than two horizontal asymptotes?
    I just want to know for sure.
    Last edited by adhesive; February 5th 2008 at 07:26 PM.
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  2. #2
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    Quote Originally Posted by adhesive View Post
    ...have more than two horizontal asymptotes?
    I think its because the graph can only have an asymptote as one of its boundaries, and a graph can only be bounded on two sides. I just want to know for sure.
    You find horizontal asymptotes by considering the limiting behavior of y = f(x) as x approaches +oo and -oo:

    If \lim_{x \rightarrow -\infty} f(x) = a then  y \rightarrow a and the line y = a is a horizontal asymptote.

    If \lim_{x \rightarrow +\infty} f(x) = b then  y \rightarrow b and the line y = b is a horizontal asymptote.

    When they exist, the values of a and b are unique by the 'uniquesness of a limit theorem'.

    Therefore there are no more than two possible horizontal asymptotes.

    Stick at it
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