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Math Help - Identifying x-intercepts and vertical asymptotes of a graph

  1. #1
    Senior Member vaironxxrd's Avatar
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    Identifying x-intercepts and vertical asymptotes of a graph

    I have the following function

    y = \frac{2x^2-7x-4}{x+5}

    X intercepts =
    0 = 2x^2-7x-4

    (x-4)(2x+1)
    x intercepts are 4, and -\frac{1}{2}

    Vertical asymptotes =

    0 = x+5

    x = -5

    Vertical asymptote is were x= -5

    Is this correct?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Identifying x-intercepts and vertical asymptotes of a graph

    Quote Originally Posted by vaironxxrd View Post
    Is this correct?
    Yes, it is correct. Only one thing, x=-5 is a vertical asymptote not only because x+5=0, we need to prove \lim_{x\to -5}y=\infty (very easy in this case). For example, x=-5 is not a vertical asymptote of y=\dfrac{x^2-25}{x+5} although x+5=0.
    Thanks from vaironxxrd
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