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Math Help - Graph?

  1. #1
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    Graph?

    what does the this look like in a graph. ((x-1)(x+2))/(x(x^2-4))
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  2. #2
    Super Member

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    Hello, darcalman!

    Graph: . y \;=\;\frac{(x-1)(x+2)}{x(x^2-4)}
    The function can be reduced . . .

    . . y \;=\;\frac{(x-1)(x+2)}{x(x-2)(x+2)} \;=\;\frac{x-1}{x(x-2)}\quad\hdots provided x \neq -2

    and there is a "hole" in the graph at \left(-2,-\frac{3}{8}\right)


    With y \:=\:\frac{x-1}{x(x-2)}, the x-intercept is (1,0).

    There are vertical asymptotes: . x = 0 and x = 2

    As x becomes extremely large, y approaches zero.
    . . There is a horizontal asymptote: y = 0 (x-axis).

    Test various values of x and determine when the graph is above or below the x-axis.


    Code:
                :         |         :
                :         |         :*
                :         |         :
                :         |*        : *
                :         |         :   *
                :         | *       :     *
                :         |  *      :           *
      - - - - - : - - - - + - -*- - : - - - - - - - -
          *     :         |      *  :
                o         |       * :
                :   *     |         :
                :      *  |        *:
                :       * |         :
                :         |         :
                :        *|         :
                :         |         :
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