Application, Domain, and Range
Application (R(x))
R(x) gives the output y such that (x, y) is in the relation R, if there is exactly one such y.
Otherwise it is undefined.
Example: f(4) = 6, but f(5) is undefined
Domain
The domain is all inputs x that appear in the relation.
dom(R) = { x | there exists y such that (x, y) ∈ R }
Example: dom(f) = {0,1,2,3,4}
Range
The range is all outputs y that appear in the relation.
ran(R) = { y | there exists x such that (x, y) ∈ R }
Example: ran(f) = {2,3,4,5,6}
Example: Function g
g(x) = (x + 3) mod 5
dom(g) = N
ran(g) = {0,1,2,3,4}
Key Idea
- Domain = all possible inputs
- Range = all possible outputs