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Math Help - Graphing the reciprocal of a cubic function

  1. #1
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    Graphing the reciprocal of a cubic function

    Hi there,

    Currently I am taking an independant learning class to earn my grade 12 Advanced Functions credit. Recently I've been learning about sketching reciprocal functions and determining where horizontal and vertical asymptotes will occur. I am very stuck on one question in particular:

    Determine the vertical asymptotes of g(x) = x + 2 / x^3 - x^2 - x + 1 and sketch the graph near the asymptotes.

    I'm not even sure how to start here, normally I would find the asymptotes by setting the denominator equal to zero, however I do no know how to solve 0 = x^3 - x^2 - x + 1

    Any help here would be much appreciated, thanks in advance!
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  2. #2
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    Re: Graphing the reciprocal of a cubic function

    Quote Originally Posted by Lethargic View Post
    Hi there,

    Currently I am taking an independant learning class to earn my grade 12 Advanced Functions credit. Recently I've been learning about sketching reciprocal functions and determining where horizontal and vertical asymptotes will occur. I am very stuck on one question in particular:

    Determine the vertical asymptotes of g(x) = x + 2 / x^3 - x^2 - x + 1 and sketch the graph near the asymptotes.

    I'm not even sure how to start here, normally I would find the asymptotes by setting the denominator equal to zero, however I do no know how to solve 0 = x^3 - x^2 - x + 1

    Any help here would be much appreciated, thanks in advance!
    Let p(x) = x^3 - x^2 - x + 1. By inspection, p(1) = 0 therefore x - 1 is a factor of x^3 - x^2 - x + 1. Divide x^3 - x^2 - x + 1 by x - 1 using polynomial long division to get the other quadratic factor. Find the zeros of the quadratic factor in the usual way.
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  3. #3
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    Re: Graphing the reciprocal of a cubic function

    Thanks!

    I actually just learned polynomial long division 2 lessons ago, I can't believe I didn't think of that
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