A function for which f(x + y) = f(x) + f(y). For example, f(x) = 3x is an additive function since f(x + y) = 3(x + y) = f(x) + f(y) but $g(x)=\sqrt{x}$ is not additive since $\sqrt{x+y}$ is not in general equal to $\sqrt{x}+\sqrt{y}$. Compare subadditive, superadditive.