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No, there cannot be any.
Probably because polynomials and convergent power series in which all terms have even degree are even functions, and similarly for odd.
An even function is symmetric about the y-axis. The graph to the left of the y-axis can be reflected onto the graph to the right. An odd function is anti-symmetric about the origin. The graph to the left of the y-axis must be reflected in the y-axis as well as in the x-axis (either one can be done first).
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.
yes