Codomain & Range: Difference & Examples

[Miike012]

≤What's the differnece between codomain and range?


Is the range a subset of the codomain?

And the codomain basically contains all possible values or elements the set R (Range) can contain?

For example:
Let f(x) = x + 1 be a function from the set of real numbers (0≤x≤4) to the set of integers.

Codomain = Set of integers
Range = 1≤f(x)≤5 where f(x) is an integer.

Now what if
f(x) = x + 1.1 be a function from the set of integers (0≤x≤4) to the set of integers.
Then is the range an empty set?

 

[Miike012]

One more question.
If the range is equal to the codomain then the function is onto?