Why is Y-axis symmetry referred to as even, Origin symmetry odd, while X-axis is called nothing?

Answer 1

Even symmetry abouy y-axis: f(x) = f(-x)
Odd symmetry about y-axis: f(x) = -f(-x) (symmetry with respect to the origin)

In well-behaved functions, there is only one value of y = f(x) for each value of x, therefore there can be no symmetry about the x axis,

Answer 2

Because x-axis symetry is not a function.