The Codomain is the set of values that could possibly come out. TheCodomain is actually part of the definition of the function. And The Range is the set of values that actually do come out. Example: we can define a function f(x)=2x with a domain andcodomain of integers (because we say so).The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.