Q:

Express the range of a Domain Subset [Notation]

I got a Function f with Domain A and Range B, if S is a subset of A, how can I express the set of the computed values of s with function f?. 

A:

$f(S)$ is a good option.  
Formally every function $f:A\rightarrow B$ induces a function $\wp\left(f\right):\wp\left(A\right)\rightarrow\wp\left(B\right)$ by:
$S\mapsto\left\{ f\left(s\right)\mid s\in S\right\} $ for $S\subset A$. 
So if ambiguity can arise you could use $\wp\left(f\right)\left(S\right)$.

