To determine the domain and range for the given set of relations [tex]\(\{(1, -8), (9, 9), (0, -8), (9, 1), (1, 8)\}\)[/tex], we'll follow the steps below:
### Step 1: Identify the Domain
The domain of a relation is the set of all possible first elements (x-coordinates) from each ordered pair in the set.
- Look at the first element of each ordered pair:
- From [tex]\((1, -8)\)[/tex], the first element is [tex]\(1\)[/tex].
- From [tex]\((9, 9)\)[/tex], the first element is [tex]\(9\)[/tex].
- From [tex]\((0, -8)\)[/tex], the first element is [tex]\(0\)[/tex].
- From [tex]\((9, 1)\)[/tex], the first element is [tex]\(9\)[/tex].
- From [tex]\((1, 8)\)[/tex], the first element is [tex]\(1\)[/tex].
- Now, collect all unique first elements to form the domain:
- The unique elements are [tex]\(1\)[/tex], [tex]\(9\)[/tex], and [tex]\(0\)[/tex].
So the domain is:
[tex]\[
\{0, 1, 9\}
\][/tex]
### Step 2: Identify the Range
The range of a relation is the set of all possible second elements (y-coordinates) from each ordered pair in the set.
- Look at the second element of each ordered pair:
- From [tex]\((1, -8)\)[/tex], the second element is [tex]\(-8\)[/tex].
- From [tex]\((9, 9)\)[/tex], the second element is [tex]\(9\)[/tex].
- From [tex]\((0, -8)\)[/tex], the second element is [tex]\(-8\)[/tex].
- From [tex]\((9, 1)\)[/tex], the second element is [tex]\(1\)[/tex].
- From [tex]\((1, 8)\)[/tex], the second element is [tex]\(8\)[/tex].
- Now, collect all unique second elements to form the range:
- The unique elements are [tex]\(-8\)[/tex], [tex]\(9\)[/tex], [tex]\(1\)[/tex], and [tex]\(8\)[/tex].
So the range is:
[tex]\[
\{-8, 9, 1, 8\}
\][/tex]
### Final Answer
- The domain is [tex]\(\{0, 1, 9\}\)[/tex].
- The range is [tex]\(\{-8, 9, 1, 8\}\)[/tex].
Thus, the domain is [tex]\(\{0, 1, 9\}\)[/tex].
