If f is a function from A to B and SA then f(S) is a subset of B and is defined

f(S) = { f(s) | s S }.

Suppose A={0,1,2,...,9} and f(a) = a+10. If B={10,11,12,...,19} or any set containing this set then f is a function from A to B.

If S={2,4,6} then f(S)={12,14,16} and f(S)B.