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Math Help - intercepts and asymptotes

  1. #1
    Junior Member
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    intercepts and asymptotes

    Sketch a graph of the given rational function. Identify any intercepts and any asymptotes.

    f(x)=2x+6/x-4

    Vertical Asymptote:
    x-4=0
    4=x

    Horizontal Asymptote:
    y=2

    x-intercept:
    2x+6=0
    3=x
    (3,0)

    y-intercept:
    f(0)=2(0)+6/0-4
    =3/-2
    (0,3/-2)

    I don't know if this is right. Now I just don't know where to plot the points. I need help with this. Thank you in advance.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by theevilp0ptart View Post
    Sketch a graph of the given rational function. Identify any intercepts and any asymptotes.

    f(x)=2x+6/x-4

    Vertical Asymptote:
    x-4=0
    4=x

    Horizontal Asymptote:
    y=2

    x-intercept:
    2x+6=0
    3=x
    (3,0)

    y-intercept:
    f(0)=2(0)+6/0-4
    =3/-2
    (0,3/-2)

    I don't know if this is right. Now I just don't know where to plot the points. I need help with this. Thank you in advance.
    Vet. Asymp. at x=4 the bottom is 0 but the tops isnt so it is a vert asymp.

    Horiz. asymp. \lim_{x \to {\pm\infty}}\frac{2x+6}{x-4}=2...so there is a horiz. asymp at y=2

    x-int...only when numerator is zero so 2x+6=0\Rightarrow{x=-3}

    y-int... f(0)=\frac{-3}{2}
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