Suppose you have a function $f$ on $\mathbb{R}^m$ with the property that for any constant $c$, you can add that constant to all of the arguments without changing the value of the function.
Formally, for all $x\in\mathbb{R}^m$, $c\in \mathbb{R}$,
$$f(x_1,\ldots, x_m) = f(x_1+c,\;\ldots,\;x_m+c).$$
Is there a name for this kind of “translation” invariance?