To determine the domain and range of the relation \( T = \{(7,7), (4,9), (0,-7), (-9,4)\} \), we will analyze the given set of ordered pairs.
Step-by-step solution:
1. Identify the domain:
- The domain of a relation is the set of all first elements (x-coordinates) in the ordered pairs.
- For the relation \( T \), we extract the first element from each pair:
- From \((7,7)\), the first element is \( 7 \).
- From \((4,9)\), the first element is \( 4 \).
- From \((0,-7)\), the first element is \( 0 \).
- From \((-9,4)\), the first element is \(-9 \).
- Thus, the domain is:
[tex]\[
\{0, 4, 7, -9\}
\][/tex]
2. Identify the range:
- The range of a relation is the set of all second elements (y-coordinates) in the ordered pairs.
- For the relation \( T \), we extract the second element from each pair:
- From \((7,7)\), the second element is \( 7 \).
- From \((4,9)\), the second element is \( 9 \).
- From \((0,-7)\), the second element is \(-7 \).
- From \((-9,4)\), the second element is \( 4 \).
- Thus, the range is:
[tex]\[
\{9, 4, -7, 7\}
\][/tex]
Final answers in set notation:
- The domain of \( T \) is:
[tex]\[
\{0, 4, 7, -9\}
\][/tex]
- The range of \( T \) is:
[tex]\[
\{9, 4, -7, 7\}
\][/tex]
