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Math Help - [SOLVED] Symmetry problems-help please!

  1. #1
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    [SOLVED] Symmetry problems-help please!

    Algebraically determine the symmetry of the following:




    I'm not quite sure what to do, please help.

    Thanks!
    Last edited by gobbajeezalus; February 23rd 2009 at 01:07 PM.
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  2. #2
    MHF Contributor

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    An expression is "symmetric about the x-axis" if replacing x by -x gives exactly the same result. For example, y= x^2 is symmetric about the x-axis because replacing x by -x you get y= (-x)^2= x^2, the same as before.

    An expression is "symmetric about the y-axis" if replacing y by -y gives exactly the same result. For example, |y|= x is symmetric about the y-axis because replacing y by -y gives |-y|= |y|= x.

    An expression is "symmetric through the origin" if replacing both x and y by -x and -y, respectively gives the same thing. It is easy to see that any expression that is both "symmetric about the x-axis" and "symmetric about the y-axis" is necessarily "symmetric through the origin. x^2+ y^2= 1 and |x|+ |y|= 1 are examples. However, xy= 1 is symmetric through the origin but not symmetric with respect to the x-axis or y-axis.
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