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Math Help - Intercepts and Aysmptotes

  1. #1
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    Intercepts and Aysmptotes

    I have got a confusing question that does not lead me to any solution. I also got a sketch a graph but unfortunately I dont have a graphical calculator. The question is given below. All help would be welcomed! This question is really confusing me..... Pls help.....

    The question is :

    Draw a careful sketch, showing and labeling all intercepts and asymptotes of
    y = x^3 + 2x^2- x - 2 / x^2 + x - 6
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  2. #2
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    Quote Originally Posted by vikas3296 View Post
    I have got a confusing question that does not lead me to any solution. I also got a sketch a graph but unfortunately I dont have a graphical calculator. The question is given below. All help would be welcomed! This question is really confusing me..... Pls help.....

    The question is :

    Draw a careful sketch, showing and labeling all intercepts and asymptotes of
    y = x^3 + 2x^2- x - 2 / x^2 + x - 6
    y = \frac{x^3+2x^2-x-2}{x^2+x-6}

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

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

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


    x-intercepts ... x = -2 , x = -1 , x = 1

    y-intercept ... y = \frac{1}{3}

    vertical asymptotes ...  x = -3 , x = 2

    slant asymptote ... perform long division on the original expression to find it.
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