Find the domain and the range of the relation. Determine whether the relation is a function. \( \{(-3,0),(3,0),(-3,9),(-9,-6)\} \)

To analyze the relation \( \{(-3,0),(3,0),(-3,9),(-9,-6)\} \), we will find the domain, the range, and determine if it is a function. ### Domain The domain of a relation is the set of all first elements (x-coordinates) of the ordered pairs. From the given relation: - The first elements are: \(-3\), \(3\), \(-3\), and \(-9\). Now, we list the unique values: - Unique values: \(-3\), \(3\), \(-9\). Thus, the domain is: \[ \text{Domain} = \{-3, 3, -9\} \] ### Range The range of a relation is the set of all second elements (y-coordinates) of the ordered pairs. From the given relation: - The second elements are: \(0\), \(0\), \(9\), and \(-6\). Now, we list the unique values: - Unique values: \(0\), \(9\), \(-6\). Thus, the range is: \[ \text{Range} = \{0, 9, -6\} \] ### Is it a Function? A relation is a function if each element in the domain is associated with exactly one element in the range. In other words, no x-coordinate can be paired with more than one y-coordinate. In our relation: - The x-coordinate \(-3\) is paired with two different y-coordinates: \(0\) and \(9\). Since \(-3\) is associated with more than one y-coordinate, the relation is **not a function**. ### Summary - **Domain**: \(\{-3, 3, -9\}\) - **Range**: \(\{0, 9, -6\}\) - **Is it a function?**: No, it is not a function.