The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. The range is the set of all the second elements (or y-values).
Let's begin by identifying them from the given relation which includes the following sets of ordered pairs: (-3,3), (-2,-1), (0,-5), (2,3).
To find the domain, we can list out all of the first elements in each pair:
- From (-3,3) the first element is -3.
- From (-2,-1) the first element is -2.
- From (0,-5) the first element is 0.
- From (2,3) the first element is 2.
So, the domain of the relation is {-3, -2, 0, 2}.
Next, let's find the range by doing the same with the second elements in each pair:
- From (-3,3) the second element is 3.
- From (-2,-1) the second element is -1.
- From (0,-5) the second element is -5.
- From (2,3) again, the second element is 3.
When listing the range, we only list distinct values and do not repeat them. So, the range of the relation is {-5, -1, 3}.
Therefore, the domain of the relation {(-3,3),(-2,-1),(0,-5),(2,3)} is {-3, -2, 0, 2} and the range is {-5, -1, 3}.