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Math Help - Domain, asymptotes, and discontinuity (oh my!)

  1. #1
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    Domain, asymptotes, and discontinuity (oh my!)

    Without using a graphing calculator,
    let f(x) = x/(abs(x^2 - 9))


    (a)Write an equation for each vertical asymptote for the graph of f.
    (b)Write an equation for each horizontal asymptote for the graph of f.
    (c) Is f odd, even, or neither? Justify your answer.
    (d) Find all values of x for which f is discontinuous and classify each discontinuity as removable or non removable.
    (e) Find the domain.


    I can do a, b, d, and e after graphing, but graphing skills, without a calculator, are not my strong point.
    C, I never understood it.

    Thanks.
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  2. #2
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    Quote Originally Posted by Truthbetold View Post
    Without using a graphing calculator,
    let f(x) = x/(abs(x^2 - 9))
    (c) Is f odd, even, or neither? Justify your answer.
    C, I never understood it.
    It is odd if f(-x)=-f(x).
    Does it?
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  3. #3
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    It is odd if .
    Does it?
    There are no negatives on the denominator, because of absolute value.
    On the top, however, x as -x makes the function like -f(x).

    That seems right, though I think logic is messed up.
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