To find the domain and range of the given relation \( S = \{(9, 2), (-6, 2), (-2, -6)\} \):
1. Domain:
- The domain of a relation is the set of all first elements (x-values) from the ordered pairs.
- From the pairs \((9, 2)\), \((-6, 2)\), and \((-2, -6)\), the first elements are \(9\), \(-6\), and \(-2\).
- Therefore, the domain is the set of these first elements.
[tex]\[
\text{domain} = \{9, -6, -2\}
\][/tex]
2. Range:
- The range of a relation is the set of all second elements (y-values) from the ordered pairs.
- From the pairs \((9, 2)\), \((-6, 2)\), and \((-2, -6)\), the second elements are \(2\), \(2\), and \(-6\).
- However, in a set, we do not list duplicate elements. So, we only need one instance of each unique second element.
[tex]\[
\text{range} = \{2, -6\}
\][/tex]
Therefore, the domain and range of the relation \( S \) are:
[tex]\[
\text{domain} = \{9, -6, -2\}
\][/tex]
[tex]\[
\text{range} = \{2, -6\}
\][/tex]
