Full Idea
The 'range' of a function is the set of elements in the output set that are values of the function for elements in the original set.
Gist of Idea
The 'range' of a function is the set of elements in the output set created by the function
Source
Peter Smith (Intro to Gödel's Theorems [2007], 02.1)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.8
A Reaction
In other words, the range is the set of values that were created by the function.