The function $f:{\mathbf R} ^2 \to {\mathbf R}^2$, given by $ f(x) = \left[ \begin{array}{c} x_1-x_2\\ x_1+x_2 \end{array}\right] $, is linear.

The function $f:{\mathbf R}^2 \to {\mathbf R}^3$, given by $f(x) = (1-x_1,0,2-x_2)$ is linear.

The function $f:{\mathbf R}^3 \to {\mathbf R}$, given by $f(x) = x_2 + 2x_3 - x_1^2$, is linear.

The reverser function $f:{\mathbf R}^n \to {\mathbf R}^n$, given by $f(x_1, \ldots, x_n) = (x_n, \ldots, x_1)$, is linear.

The function $f:{\mathbf R}^n \to \mathbf R$, where $f(x)$ is the average of the entries $x_1, \ldots, x_n$, is linear.

The function $f:{\mathbf R}^n \to \mathbf R$, where $f(x)$ is the median of the entries $x_1, \ldots, x_n$, is linear.