State the domain and range of the relation. Determine whether the relation represents a function \( \{(-6,-6),(0,0),(6,6)\} \)

To determine the domain and range of the relation \( \{(-6,-6),(0,0),(6,6)\} \), we can analyze the ordered pairs. 1. **Domain**: The domain of a relation is the set of all first elements (x-coordinates) of the ordered pairs. For the given relation: - The first elements are: \(-6\), \(0\), and \(6\). - Therefore, the domain is: \[ \text{Domain} = \{-6, 0, 6\} \] 2. **Range**: The range of a relation is the set of all second elements (y-coordinates) of the ordered pairs. For the given relation: - The second elements are: \(-6\), \(0\), and \(6\). - Therefore, the range is: \[ \text{Range} = \{-6, 0, 6\} \] 3. **Function Check**: A relation is a function if each element in the domain is associated with exactly one element in the range. In this case: - Each x-coordinate \(-6\), \(0\), and \(6\) is paired with exactly one y-coordinate \(-6\), \(0\), and \(6\) respectively. - There are no repeated x-coordinates. Since each x-coordinate corresponds to exactly one y-coordinate, the relation does represent a function. **Summary**: - Domain: \(\{-6, 0, 6\}\) - Range: \(\{-6, 0, 6\}\) - The relation represents a function.