What is a Function?
Definition: A function is a correspondence between two sets, the domain and the ranges, such that for each value in the domain there corresponds exactly one value in the range.

Distinct Features of a Function
The set x is the domain.
The set y is the range or co-domain.
f assigns only one element y E Y to each x E X.
y = f(x) denotes the functional value y at x.
Observe the figure below. f transforms the domain X, element by element, int the range or co-domain Y.
Figure 1