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Math Help - rational functions

  1. #1
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    rational functions

    sorry for asking this again, i need to finish this by today so that i can submit this by tom..

    Sketch the graph of function Q(x) = x^3 - 1 / x^3 + 1. Determine the prime
    factorization of Q(x) and graph the polynomial function.

    Thanks !
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  2. #2
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    Quote Originally Posted by woooo View Post
    sorry for asking this again, i need to finish this by today so that i can submit this by tom..

    Sketch the graph of function Q(x) = x^3 - 1 / x^3 + 1. Determine the prime
    factorization of Q(x) and graph the polynomial function.

    Thanks !
    Key features:

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

    y-intercept: Substitute x = 0 and solve for y.

    x-intercept: Substitute y = 0 and solve for x. So solve x^3 - 1 = 0.

    Vertical asymptote: By inspection, x = -1.

    Horizontal asymptote: By inspection, y = 1.

    x-coordinates of stationary points: Solve Q'(x) = 0. So solve \frac{6x^2}{(x^3 + 1)^2}[/tex]. Test nature. Now get y-coordinates.

    Now draw the shape that fits the above features.

    Edit: And please DON'T double post.
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