Q:

How is a corelation of function inputs to its outputs is called in math?

So I  have a function $f$ and for a set of argument intervals I have a set of its result intervals?
Example: say for $f(x)$ I have $f(2..6) = -1..2$ and $-inf..+inf$ for all others (ones I do not care about or do not have info). 
How calculation and operatoion on such intervals is called?

A:

Image (mathematics).
I don't know if operations on images hava a special name, though; they are just sets to be transformed or whatever.

