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Math Help - Odd / Even Functions.

  1. #1
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    Exclamation Odd / Even Functions.

    Hi, I have a test on pre calc topics on Monday in my Calc class.
    I am reviewing odd and even functions right now.
    Here is the problem: True or False: The function f(x)= x^-3 is an odd function.

    I have true and this is what i did to prove it:

    (-x)^-3 = -x since it equals -x it's odd right?

    But then I graphed it on my graphing calculator and it did not look right O_o... am I doing something wrong? Can i be neither?
    Last edited by mr fantastic; September 11th 2010 at 03:57 PM. Reason: Edited title.
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by habibixox View Post
    Hi, I have a test on pre calc topics on Monday in my Calc class.
    I am reviewing odd and even functions right now.
    Here is the problem: True or False: The function f(x)= x^-3 is an odd function.

    I have true and this is what i did to prove it:

    (-x)^-3 = -x since it equals -x it's odd right?

    But then I graphed it on my graphing calculator and it did not look right O_o... am I doing something wrong? Can i be neither?
    if function

     f(-x) = -f(x)

    function is odd.

    if function

     f(-x) = f(x)

    function is even.

    if function is

     f(-x) \neq  f(x) and  f(-x) \neq -f(x) than function is neither odd neither even

     f(x) = x^{-3} = \frac {1}{x^3 }

     f(-x) = - \frac {1}{x^3} = - f(x)

    so it's odd function


    and here you are graph of that odd function
    Attached Thumbnails Attached Thumbnails Odd / Even Functions.-oddfunction.jpg  
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