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an equation is being tested for symmetry with respect to the x-axis, the y-axis, and the origin. explain why, if two of these symmetries are present then remaining one must also be present.

  • math - ,

    For x-axis reflection symmetry,
    f(x,y) = f(x,-y)

    For y-axis reflection symmetry,
    f(x,y) = f(-x,y)

    For symmetry about the origin,
    f(x,y) = f(-x,-y)

    If you reflect about both x and y axes, it is equivalent to reflecting about the origin.

    If you reflect about the origin and then one axis, you have reflected about the other axis.

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