Which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)?

A vertical translation adds a constant: the new function is f(x) + c. If f is even, f(−x) = f(x), so adding the same constant keeps that equality true. But for an odd function, g(−x) = −g(x); adding a nonzero constant generally breaks this relationship. Therefore, vertical translation preserves even symmetry but not odd symmetry.

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