What is the property called wherein permuting the input tuple of a function results in the same permutation in the output tuple?

Question

A function f takes an n-tuple as input and gives an n-tuple as output.

If permuting the elements of the input n-tuple of this function always results in the same permutation of the elements of the output n-tuple of this function, what is this property called?

For example, if $f(x_1, x_2, x_3) = (y_1, y_2, y_3)$, then $f(x_1, x_3, x_2) = (y_1, y_3, y_2)$.