Equation

Is x⁵ - 3y⁵ - 9 = 0 symmetrical to the x axis, y axis, origin or all three?

To test for y axis symmetry substitute -x in for every x.   If the resulting equation is the same then
it is symmetrical to the y axis:   (-x)⁵ - 3y⁵ - 9 = 0
  →   -x⁵ - 3y⁵ - 9 = 0   
The results are not the same as the original equation and hence the equation is not symmetrical to the y axis.   

To test for x axis symmetry substitute -y in for every y:  x⁵ - 3(-y)⁵ - 9 = 0    →   x⁵ + 3y⁵ - 9 = 0
The results differs from the original equation hence it is not symmetrical to the x axis.

To test for origin symmetry substitute -y in for every y and -x for every x:   (-x)⁵ - 3(-y)⁵ - 9 = 0   →  (-x)⁵ + 3y⁵ - 9 = 0   
The results differs from the original equation hence it is not symmetrical to the origin.

This equation is not symmetrical to the x axis, y axis or origin.
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