To determine the domain and range of the function described by the set [tex]\(\{(-2,2),(0,3),(-1,2),(-3,4),(1,-3)\}\)[/tex], let's follow these steps:
1. Identifying the Domain:
- The domain of a function is the set of all possible input values (the [tex]\(x\)[/tex]-coordinates).
- From the given pairs [tex]\((-2, 2)\)[/tex], [tex]\((0, 3)\)[/tex], [tex]\((-1, 2)\)[/tex], [tex]\((-3, 4)\)[/tex], and [tex]\((1, -3)\)[/tex], we collect the [tex]\(x\)[/tex]-coordinates:
[tex]\[
\{-2, 0, -1, -3, 1\}
\][/tex]
2. Identifying the Range:
- The range of a function is the set of all possible output values (the [tex]\(y\)[/tex]-coordinates).
- From the same pairs, we collect the [tex]\(y\)[/tex]-coordinates:
[tex]\[
\{2, 3, 2, 4, -3\}
\][/tex]
- Notice that the value [tex]\(2\)[/tex] repeats, but in set notation, we list each element only once. Therefore, the range is:
[tex]\[
\{2, 3, 4, -3\}
\][/tex]
Thus, the domain and range of the function are:
- Domain: [tex]\(\{-3, -2, -1, 0, 1\}\)[/tex]
- Range: [tex]\(\{2, 3, 4, -3\}\)[/tex]
Based on the provided answers, the correct choice is:
Domain: [tex]\(\{-3, -2, -1, 0, 1\}\)[/tex]
Range: [tex]\(\{2, 3, 4, -3\}\)[/tex]
