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Math Help - Help Graphing a Polynomial

  1. #1
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    Post Help Graphing a Polynomial

    How do I graph this Polynomial?
    I need to also show the asymptotes and hole(s).

    F(x)= (-(x^4)-(3x^3)-7x-21) / ((x^3)-(7x^2)-5x-75)
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  2. #2
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    Quote Originally Posted by Kairo View Post
    How do I graph this Polynomial?
    I need to also show the asymptotes and hole(s).

    F(x)= (-(x^4)-(3x^3)-7x-21) / ((x^3)-(7x^2)-5x-75)
    If you can factor a polynomial from both numerator and denominator, there will be a hole in the graph. If when you factor nothing cancels, the real roots of the denominator will have vertical asymptotes.

    Since the numerator has a higher power, you will have a slant asymptote. You can solve that by long division; furthermore, the SA will be the solution to the division disregarding any remainders.
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  3. #3
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    The first thing you should know is that this is not a polynomial! It is a "rational function". Asymptotes occur where the denominator is 0 but the numerator isn't. "Holes" occur where both numerator and denominator are 0.
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    The first thing you should know is that this is not a polynomial! It is a "rational function". Asymptotes occur where the denominator is 0 but the numerator isn't. "Holes" occur where both numerator and denominator are 0.
    I never said the function as a whole was a polynomial. If we look at the numerator and denominator independently, we have two polynomials. If those polynomials happen to factor to a form of (x-2)(...)/(x-2)(!!!), then where ever the factors cancel there will be hole in the graph. Sorry for no latex but I am on my phone.
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