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

Answer 1

Because being symmetrical on the x-axis has nothing to do with making the f(x) negative or not; rather, by chaninging the 'y' of the equation, you will make it x-axis symmetrical.

I think the correlation between x-axis and y-axis symmetry and being odd or even isn't directly related; they are just properties of graphing.

Hope I didn't lose ya.

Answer 2

Even symmetry is f(-x) = f(x), and the axis of symmetry is the y axis
Odd symmetry is f(x) = -f(-x), and the symmetry is rotational around the origin. A single-valued function can have no symmetry about the x axis, because it exists only on one side or the other, but not both. (I think I answered this before.)