To find the domain and range of the relation [tex]\(Q = \{(-2, 4), (0, 2), (-1, 3), (4, -2)\}\)[/tex]:
### Calculating the Domain
The domain of a relation is the set of all first coordinates (or input values) from each ordered pair.
1. Look at the first elements of each pair:
- From [tex]\((-2, 4)\)[/tex], the first element is [tex]\(-2\)[/tex].
- From [tex]\((0, 2)\)[/tex], the first element is [tex]\(0\)[/tex].
- From [tex]\((-1, 3)\)[/tex], the first element is [tex]\(-1\)[/tex].
- From [tex]\((4, -2)\)[/tex], the first element is [tex]\(4\)[/tex].
2. Collect these first elements together to form the domain:
- The domain is [tex]\(\{-2, 0, -1, 4\}\)[/tex].
Writing it in ascending order, the domain is:
[tex]\[\{-2, -1, 0, 4\}\][/tex]
### Calculating the Range
The range of a relation is the set of all second coordinates (or output values) from each ordered pair.
1. Look at the second elements of each pair:
- From [tex]\((-2, 4)\)[/tex], the second element is [tex]\(4\)[/tex].
- From [tex]\((0, 2)\)[/tex], the second element is [tex]\(2\)[/tex].
- From [tex]\((-1, 3)\)[/tex], the second element is [tex]\(3\)[/tex].
- From [tex]\((4, -2)\)[/tex], the second element is [tex]\(-2\)[/tex].
2. Collect these second elements together to form the range:
- The range is [tex]\(\{4, 2, 3, -2\}\)[/tex].
Writing it in ascending order, the range is:
[tex]\[\{ -2, 2, 3, 4 \}\][/tex]
### Final Answer:
Domain: [tex]\(\{ -2, 0, -1, 4 \}\)[/tex]
Range: [tex]\(\{ 2, 3, 4, -2 \}\)[/tex]
