To find the domain and range of the given relation \({(9, 3), (-6, -3), (1, -1), (3, -7)}\), we will extract the values of the first and second elements of each ordered pair.
Domain: The domain consists of the first elements of the ordered pairs:
- From \((9, 3)\), we take \(9\)
- From \((-6, -3)\), we take \(-6\)
- From \((1, -1)\), we take \(1\)
- From \((3, -7)\), we take \(3\)
Thus, the domain is: \[ {9, -6, 1, 3} \]
Range: The range consists of the second elements of the ordered pairs:
- From \((9, 3)\), we take \(3\)
- From \((-6, -3)\), we take \(-3\)
- From \((1, -1)\), we take \(-1\)
- From \((3, -7)\), we take \(-7\)
Thus, the range is: \[ {3, -3, -1, -7} \]
Function Check: A relation is a function if each element of the domain is associated with exactly one element in the range. Since all the first elements (9, -6, 1, 3) are unique in the given ordered pairs, this relation is indeed a function.
Final Answers:
- The domain is \({9, -6, 1, 3}\).
- The range is \({3, -3, -1, -7}\).
- The relation is a function.