Suppose that the relation [tex]T[/tex] is defined as follows.

[tex]T = \{(7,7), (4,9), (0,-7), (-9,4)\}[/tex]

Give the domain and range of [tex]T[/tex]. Write your answers using set notation.

Domain [tex]= \square[/tex]

Range [tex]= \square[/tex]



Answer :

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]