Let $\map f x$ be the real function defined as:

$\forall x \in \R: \map f x = 3 x$

Then $f$ is an additive function.

## Proof

 $\displaystyle \map f {x + y}$ $=$ $\displaystyle 3 \paren {x + y}$ $\displaystyle$ $=$ $\displaystyle 3 x + 3 y$ $\displaystyle$ $=$ $\displaystyle \map f x + \map f y$

$\blacksquare$