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Math Help - Curve Sketching

  1. #1
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    Curve Sketching

    For my project, I have to pick an equation and sketch it.
    I picked (x^2-3x+4)/(x^2+2x-1) and I found that there is a horizontal asymptote at y=1. But when I plug in 1 in to the equation there is a point at (1,1). How does that happen?
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  2. #2
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    Hello, dimpleyy!

    A common misunderstanding . . .
    (I went through it myself many years ago.)


    For my project, I have to pick an equation and sketch it.
    I picked: . y \:=\:\frac{x^2-3x+4}{x^2+2x-1}
    and I found that there is a horizontal asymptote at y=1.
    But when I plug in 1 in to the equation there is a point at (1,1).
    How does that happen?

    A horizontal asymptote indicates the behavior of f(x) for large values of x.

    That is, as we go to the far right (or far left), the graph approaches y = 1.

    However, locally, the function can have y = 1.

    The graph might look like this . . .
    Code:
                    |
                    |        *
                    |     *    *
                    |   *       *
                    |  *           *
                    | *                 *
                    |                          *
          - - - - - +o- - - - - - - - - - - - - - - -
                    |
         -----------*------------------------------------
                    |
                    |
                   *|
                    |
                  * |
                 *  |


    You see, the graph can cross the horizontal asymptote.
    . . The asymptote takes over on extreme values only.

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