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Math Help - Symmetric about the origin

  1. #1
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    Symmetric about the origin

    Hi all,

    Can someone please help me understand how the following function is symmetric about the origin?

    y = 3x /(x^2 + 9)

    -y = 3(-x) / (-x)^2 + 9
    -y = -3x / x^2 + 9 (multiply numerator and denominator by -1)
    y = 3x/ -x^2 -9

    The functions are not the same yet, in the back of my book it says that it is symmetric about the origin.
    Thanks for the help,

    Alex
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Symmetric about the origin

    If the function is odd, then it is symmetric about the origin, i.e. f(-x)=-f(x).

    Any function of the form:

    f(x)=\frac{ax}{bx^2+c} where a,b,c are constants and a and b are not both zero

    is an odd function, since:

    f(-x)=\frac{a(-x)}{b(-x)^2+c}=-\frac{ax}{bx^2+c}=-f(x)
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