Are all odd functions symmetric about the orizin?

Yes, all odd functions are symmetric about the origin. This means that for any point ((x, f(x))) on the graph of an odd function, the point ((-x, -f(x))) will also be on the graph. This symmetry is defined by the property (f(-x) = -f(x)) for all (x) in the function's domain. Thus, the graph of an odd function exhibits rotational symmetry around the origin.