Exponential Function is Superfunction

Theorem
The function $f : \C \to \C$, defined as
 * $f \left({ z }\right) = c^z$

is a superfunction for any complex number $c$.

Proof
Define $h : \C \to \C$ by $h \left({ z }\right) = z \times c$. Then

Thus $f \left({z}\right) = c^z$ is a superfunction and $h \left({z}\right) = z \times c$ is the corresponding transfer function.