Binary function which added to itself, arguments switched, gives a constant

Question

Say I have the function $$ f_1(x, y) = \frac{x}{x + y} \label{a}\tag{1} $$ or $$ f_2(x, y) = \frac{y - x}{x + y} \label{b}\tag{2} $$ or $$ f_3(x, y) = x - y \label{c}\tag{3} $$

Then $f(a, b) + f(b, a) = c$ for any $a$ and $b$.

Is there a name for such a property?
If there is no short name for it, how would you describe it?

So far I've said that the function and its commutation(?) are additively inverse, around some value $d = c/2$. In the case of $(\ref{b})$ and $(\ref{c})$ that value would be $0$, in $(\ref{a})$ it would be $0.5$

Answer 1

In the special case when $c=0$ it's called an alternating function. I don't think it has a name for general $c$.

We do have in general that $f(x,y)-\frac c2$ is alternating, though.