Date: 2008-02-29 08:16 pm (UTC)
Yes, f(x)=0 is the only function that is symmetric with respect to the X-axis, the requirement being f(x) = -f(x) (rather than f(x) = f(-x), which is symmetry with respect to the Y-axis, or f(x) = -f(-x), which is probably symmetry with respect to the line y=-x but which I'd just call an odd function)
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