Define a function as a set of ordered pairs.

Function as a set of ordered pairs: A function is a set of ordered pairs with the property that no two ordered pairs have the same first component and a different second component. 

The domain of a function is the set of all first components, x, in the ordered pairs and the range of a function is the set of all second components, y, in the ordered pairs.

For. e.g. $\{(1, x),(2, y),(3, z)\}$ is a function, since there are no two pairs with the same first component.

Here, Domain is {1, 2, 3} and Range is {x, y, z}