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Asymtotes and polynomials

  1. Dec 17, 2004 #1
    Ok, I have a final in Pre-Calc comming up, and im still a bit confused on finding asymtotes (vertical, horizontal, and slant) could someone help me with equations i can use to find the asymtotes or how i do? im just really confused.

    Heres the problem. Find the vertical asymtote(s): F(x) = X+3 / (X-2)(X+5)

    I dont even have a start because im so confused :confused:

    Also, I am having trouble with finding a fourth degree polynomial that has a set of given zeros. How might i go about solving one of those? Im very confused, please help me

    The problem Find a fourth Degree polynomial that has zeros: 1, -3, 2i

    Once again i have no clue where to start...a little help please?
  2. jcsd
  3. Dec 17, 2004 #2
    The vertical asymptotes occur when F(x) tends to infinity. You should be able to see these clearly as they're when the denominator is 0. There are two of them; one at x = 2 and one at x = -5.

    For the second bit, you need to use the factor theorem. You know that if f(a) = 0, then (x - a) is a factor. You also know that if one complex number is a root, then its complex conjugate is also a root. Can you go from there?
    Last edited: Dec 17, 2004
  4. Dec 17, 2004 #3
    Vertical asymptotes - look for the number that makes the denominator = 0

    Horizontal Asymptotes - If the degree of the powers are equal, take the coefficients of them and you have y = a/b. If the power in the denominator is larger than the one in the numerator, then you have a H.A. at y=0

    Slant Asymptotes - If the power in the numerator is 1 degree larger than the denominator, then you divide the bottom into the top. (ex. x^2 / (x-1))

    If the power in the numerator is more than 1 degree higher than the denominator, then there is no H.A.!
  5. Dec 17, 2004 #4


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    There is an easier method to finding these. It covers basically what was said above but uses more conventional methods.

    Vertical Asymptote(s): X values that make the denominator zero.

    Just reverse factor the zero's and you will end with the original equation. Although be careful, with imaginary numbers. => 2i they have special conditions.
  6. Dec 17, 2004 #5


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    They dont occur when F(x) tends to infinity, that is the limit as x approaches positive infinity and as a way to find the Horizontal asymptote. You need to specify the use of only the highest degree terms in the numerator and denominator.
  7. Dec 17, 2004 #6
    Not sure I understand. You find vertical asymptotes where the denominator is zero and division by zero should be infinity?
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