If I recall correctly a function of x *must* have a *single* value for all values of x (except at singular points where the limit depends on the direction of approach -- think tan(pi/2))
If symmetry requires that every point have a corresponding point eqi-distant from the x axis in the opposite direction, then y=0 is not symmetric, as there is only a single point corresponding to each x value.
I'm not sure that there is a valuable answer. Certainly not without a rigorous definition of both function and symmetry. If anybody is really keen -- seek out Joukowski Transforms that will translate a circle into a flat line of finite length where there really are two y values for each x value, but both of them are zero, except where there is no y value ;-)
Definitions....?
If symmetry requires that every point have a corresponding point eqi-distant from the x axis in the opposite direction, then y=0 is not symmetric, as there is only a single point corresponding to each x value.
I'm not sure that there is a valuable answer. Certainly not without a rigorous definition of both function and symmetry. If anybody is really keen -- seek out Joukowski Transforms that will translate a circle into a flat line of finite length where there really are two y values for each x value, but both of them are zero, except where there is no y value ;-)