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Math Help - asymptotes

  1. #1
    Junior Member
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    asymptotes

    Find the vertical asymptotes, if any, of the graph of the rational function.

    g(x) = x/x^2-36
    i got x=6, x=-6

    h(x) = x+4/x(x-2)
    i got x=2

    Find the slant asymptote, if any, of the graph of the rational function.

    f(x) = x^2+16/x
    i got y=x

    h(x) = x^3+6/x^2-25
    (this one I dont understand)

    g(x) = x^3+7/x^2+8
    (this one I dont understand)

    Graph the function.

    f(x) = x^3+4/x^2+5x
    (this one I dont understand)
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  2. #2
    MHF Contributor kalagota's Avatar
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    Taguig City, Philippines
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    [quote=soly_sol;80225]Find the vertical asymptotes, if any, of the graph of the rational function.

    g(x) = x/x^2-36
    i got x=6, x=-6

    Quote Originally Posted by soly_sol View Post
    h(x) = x+4/x(x-2)
    i got x=2
    also, x=0 is a vertical asymptote

    Find the slant asymptote, if any, of the graph of the rational function.

    f(x) = x^2+16/x
    i got y=x

    Quote Originally Posted by soly_sol View Post
    h(x) = x^3+6/x^2-25
    (this one I dont understand)

    g(x) = x^3+7/x^2+8
    (this one I dont understand)
    try to perform the division using synthetic division.

    you will get something like y=mx+b +r(x)
    that mx+b is your slant asymptote.
    so, for h(x), your asymptote is y=x.
    Quote Originally Posted by soly_sol View Post
    Graph the function.

    f(x) = x^3+4/x^2+5x
    (this one I dont understand)

    just look for the asymptotes, look for the zeros, then the limits as x approaches the asymptotes, and approaches infinity (positve, negative)
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