The only function that can do this is f(x)=0, or y=0
What about y2-x2=0
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No. In fact, no number can be both odd and even at the same time.
It can't happen.
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
Yes f(x)=0 is both even and odd
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.