Find the domain and range of the following relation. Also determine whether the relation is a function. \[ \{(4,2),(4,3),(4,5),(4,6)\} \]

To find the domain and range of the given relation \(\{(4,2),(4,3),(4,5),(4,6)\}\), we will analyze the ordered pairs. 1. **Domain**: The domain of a relation is the set of all first elements (x-coordinates) of the ordered pairs. In this case, all the ordered pairs have the same first element, which is \(4\). Therefore, the domain is: \[ \text{Domain} = \{4\} \] 2. **Range**: The range of a relation is the set of all second elements (y-coordinates) of the ordered pairs. The second elements in the given pairs are \(2\), \(3\), \(5\), and \(6\). Thus, the range is: \[ \text{Range} = \{2, 3, 5, 6\} \] 3. **Function**: A relation is considered a function if each element in the domain is associated with exactly one element in the range. In this case, the domain \(\{4\}\) is associated with multiple values in the range (\(2\), \(3\), \(5\), and \(6\)). Since the same input \(4\) corresponds to multiple outputs, this relation is **not a function**. In summary: - **Domain**: \(\{4\}\) - **Range**: \(\{2, 3, 5, 6\}\) - **Is it a function?**: No, it is not a function.