MHB Odd/Even Functions: Check Symmetry over Y Axis First

[Yankel]

Hello

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 !

 

[MarkFL]

If f(-x) = f(x), then it is symmetric about the y-axis, i.e., it is even. I think your method is best.

 

[Mr Fantastic]

Hello

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 !

Think about the transformations to f(x) represented by f(-x) and -f(x) ...