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Math Help - Please help with Rationals

  1. #1
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    Unhappy Please help with Rationals

    Hi, I have this function, g(x)= (x^3-x)/(x^3-4x).
    Now I need help with the following...
    - How to find the zeros for f?
    - How to find f(-x)?
    - How to find point of discontinuity?

    And also, would finding the asymptotes, slant asymptote, and point of discontinuity be easier if I simplify this rational first?:
    (2x^3-3x^2-12x+20)/(x^2-5x+6)
    I can simplify the denominator as (x+1)(x-6) but that's it...
    Is the first step to simplifying the numerator... Factoring out x?

    I'd appreciate any help, thanks so much!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by bubblegum View Post
    Hi, I have this function, g(x)= (x^3-x)/(x^3-4x).
    Now I need help with the following...
    - How to find the zeros for f?
    - How to find f(-x)?
    - How to find point of discontinuity?

    And also, would finding the asymptotes, slant asymptote, and point of discontinuity be easier if I simplify this rational first?:
    (2x^3-3x^2-12x+20)/(x^2-5x+6)
    I can simplify the denominator as (x+1)(x-6) but that's it...
    Is the first step to simplifying the numerator... Factoring out x?

    I'd appreciate any help, thanks so much!
    A rational functions zeros are only in the numerator...so you need to solve x^3-x=0\Rightarrow{x(x^2-1)=0}..so x=0,x=-1,x=1

    since this is odd f(-x)=-f(x)
    solve the denominator for 0 we get x(x^2-4)=0 so x=0,x=2, x=-2 all points of discontinuity

    just polynomial divide...DO NOT simplify first to find slant asymptotes
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