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Math Help - Find Asymptotes of Rational Function

  1. #1
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    Find Asymptotes of Rational Function

    Find the vertical, horizontal and obligue asymptotes, if any, of the rational function below.

    F(x) = (x -1)/(x - x^3)
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  2. #2
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    (x-1)/(x (1-x^2) = (x-1)/(x (1-x)(1+x) ) = -1/(x (1+x) )

    Take note that since we canceled 1-x, then there is a hole at x = 1. That is, f(x) is not defined at x = 1.

    There is no oblique asymptotes.

    The vertical asymptote is at x = 0 and x = -1 (These are the points that makes the function undefined).

    The horizontal asymptote is zero since the limit as x goes to infinity equals 0. In Algebra, you would probably know it by this way:

    - Degree of Numerator > Degree of Denominator, then no horizontal asymptote exist.
    - Degree of Numerator = Degree of Denominator, then horizontal asymptotes is the y = a/b, where a and b is the coefficients for the leading terms in numerator and denominator, respectively.
    - Degree of Numerator < Degree of Denominator, then horizontal asymptote is y = 0
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Chop Suey View Post
    (x-1)/(x (1-x^2) = (x-1)/(x (1-x)(1+x) ) = -1/(x (1+x) )

    Take note that since we canceled 1-x, then there is a hole at x = 1. That is, f(x) is not defined at x = 1.

    There is no oblique asymptotes.

    The vertical asymptote is at x = 0 and x = -1 (These are the points that makes the function undefined).

    The horizontal asymptote is zero since the limit as x goes to infinity equals 0. In Algebra, you would probably know it by this way:

    - Degree of Numerator > Degree of Denominator, then no horizontal asymptote exist.
    - Degree of Numerator = Degree of Denominator, then horizontal asymptotes is the y = a/b, where a and b is the coefficients for the leading terms in numerator and denominator, respectively.
    - Degree of Numerator < Degree of Denominator, then horizontal asymptote is y = 0
    The graph verifies what you have done! (Good work! )



    --Chris
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  4. #4
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    It's clear....

    Both replies are clear.

    Thanks a million!
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