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Math Help - How to find the horizontal asymptote of the following function

  1. #1
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    How to find the horizontal asymptote of the following function

    f(x)=(x-2)^5 / (x+2)^3(x-4)^3


    can someone not just show me the answer (i have that), but an easy way to get to it?


    thanks!
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by calcconfused View Post
    f(x)=(x-2)^5 / (x+2)^3(x-4)^3


    can someone not just show me the answer (i have that), but an easy way to get to it?


    thanks!
    Here are the three cases of horizontal asymptotes:

    1) If the degree of the denominator is greater than the degree of the numerator, the HA is y=0

    2) If the degrees of the numerator & denominator are the same, the HA is the ratio of the leading coefficients

    3) If the degree of the numerator is larger than the denominator there is not a HA

    In terms of finding which it is, you can factor it all out and see what the degrees of each will be.

    Hope that helps!
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  3. #3
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    that does help but can someone break it down for me a bit?


    i dont see why 1/x^6 is put in both the num and denom
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