Question

Find the domain and range of the relation: { ( 4 , − 4 ) , ( 3 , − 4 ) , ( 2 , − 4 ) , ( 1 , − 4 ) } . Then determine whether the relation is a function.

Answer 1

Domain:
`Dom\{f\} = \{1,2,3,4\}`, Range:
`Ran\{f\} = \{-4\}`

The relation is a function.

Explanation:

Let be
`f` a relation. The domain of the relation is the set of first components of ordered pairs of the relation, whereas the range of the relation is the set of second components of ordered pairs of the relation. Hence, the domain and range of the relation are, respectively:

`Dom\{f\} = \{1,2,3,4\}`

`Ran\{f\} = \{-4\}`

A relation is a function if and only if every element of the domain has only one element of the range. This is the case for this relation, since there is just an element for range.