Certainly! Let's determine the domain and range of the given relation [tex]\(\{(-2, 12), (0, 8), (1, 9), (5, 3)\}\)[/tex].
### Step-by-Step Solution:
1. Identify the Domain:
The domain of a relation is the set of all first elements (or x-values) from each ordered pair.
From the given relation, we extract:
- The first element of [tex]\((-2, 12)\)[/tex] which is [tex]\(-2\)[/tex].
- The first element of [tex]\((0, 8)\)[/tex] which is [tex]\(0\)[/tex].
- The first element of [tex]\((1, 9)\)[/tex] which is [tex]\(1\)[/tex].
- The first element of [tex]\((5, 3)\)[/tex] which is [tex]\(5\)[/tex].
Therefore, the domain is [tex]\(\{-2, 0, 1, 5\}\)[/tex].
2. Identify the Range:
The range of a relation is the set of all second elements (or y-values) from each ordered pair.
From the given relation, we extract:
- The second element of [tex]\((-2, 12)\)[/tex] which is [tex]\(12\)[/tex].
- The second element of [tex]\((0, 8)\)[/tex] which is [tex]\(8\)[/tex].
- The second element of [tex]\((1, 9)\)[/tex] which is [tex]\(9\)[/tex].
- The second element of [tex]\((5, 3)\)[/tex] which is [tex]\(3\)[/tex].
Therefore, the range is [tex]\(\{3, 8, 9, 12\}\)[/tex].
Putting it all together:
- The domain is [tex]\(\{-2, 0, 1, 5\}\)[/tex].
- The range is [tex]\(\{3, 8, 9, 12\}\)[/tex].
These match with the results we have previously determined.
### Answer:
The correct choice is:
A) Domain [tex]\(=\{-2,0,1,5\}\)[/tex] Range [tex]\(=\{12,8,9,3\}\)[/tex]
