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Math Help - Sketching graph of y =(x^3-2x^2-10x-1)/(x^2-2x-15)

  1. #1
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    Sketching graph of y =(x^3-2x^2-10x-1)/(x^2-2x-15)

    Sketch the graph of the following.

    y = \dfrac{x^3-2x^2-10x-1}{x^2-2x-15}


    Any help would be appreciated!
    Last edited by mr fantastic; January 26th 2011 at 12:52 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Quote Originally Posted by Joker37 View Post
    Sketch the graph of the following.

    y = \dfrac{x^3-2x^2-10x-1}{x^2-2x-15}

    Any help would be appreciated!
    You can write it like those too to help you:

    y = \dfrac{x^3-2x^2-10x-1}{(x-5)(x+3)} = x + \dfrac{3}{x-5} + \dfrac{2}{x+3}

    You know that there are two vertical asymptotes at x = 5 and x = -3, then the graph also tends to the line y = x as x becomes large.

    Since there are two asymptotes, the graph is in three parts and as similar graphs, the central part is fairly similar to the numerator, that is a cubic.

    Now what you can do is try out what is the value of y slightly to the left and slightly to the right of the asymptotes to know the shape of the graph, whether it's ascending or descending.
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