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I have a theoretical question. When I check if a function is odd or even, I usually check:

f(x)=f(-x) or f(-x)=-f(x)

someone told me today that before checking it, I first need to check the symmetry over the Y axis, and if the function is not symmetric over Y, there is no point of checking for odd or even.

Can someone explain this to me, and give a simple example of how to check for symmetry ?

thanks !