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Math Help - Graph Sketching ARRGHH!!

  1. #1
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    Graph Sketching ARRGHH!!

    { y }^{ 2 }\quad =\quad \frac { (x+1)(x-3) }{ (x+4) }

    okay so,

    I know its symmetric about the x axis because of y^2

    y = 0 at

    x = 3 and x = -1

    graph doesn't exist when y^2 < 0

    so i did complete the square on the numerator and got

    (x - 1)^2 < 4

    so x -1 < 2

    so for x < 3 and x < -1 the graph doesn't exist

    but apparently there is an asymptote at x = - 4 and the graph does exist between -4 and -1 (I was given the answer)

    please help
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  2. #2
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    Re: Graph Sketching ARRGHH!!

    Quote Originally Posted by Applestrudle View Post
    graph doesn't exist when y^2 < 0

    so i did complete the square on the numerator and got

    (x - 1)^2 < 4
    You need to determine the sign of the right-hand side as a whole and not just its numerator. Please review how to solve rational inequalities.

    Just one remark.

    Quote Originally Posted by Applestrudle View Post
    so x -1 < 2
    $(x-1)^2<4$ is equivalent to $-2<x-1<2$ and not to $x-1<\pm2$.
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