Find the domain and range of the relation. Also determine whether the relation is a function. \[ \{(-6,5),(2,-3),(-7,-7),(-3,-3)\} \]

To find the domain and range of the given relation \(\{(-6,5),(2,-3),(-7,-7),(-3,-3)\}\), we will identify the set of all first elements (inputs) and the set of all second elements (outputs) from the ordered pairs. ### Domain The domain consists of the first elements of each ordered pair: - From \((-6, 5)\), the first element is \(-6\). - From \((2, -3)\), the first element is \(2\). - From \((-7, -7)\), the first element is \(-7\). - From \((-3, -3)\), the first element is \(-3\). Thus, the domain is: \[ \text{Domain} = \{-6, 2, -7, -3\} \] ### Range The range consists of the second elements of each ordered pair: - From \((-6, 5)\), the second element is \(5\). - From \((2, -3)\), the second element is \(-3\). - From \((-7, -7)\), the second element is \(-7\). - From \((-3, -3)\), the second element is \(-3\). Thus, the range is: \[ \text{Range} = \{5, -3, -7\} \] ### Is it a Function? A relation is a function if every element in the domain is associated with exactly one element in the range. In this case, we check the first elements (domain values): - \(-6\) maps to \(5\) - \(2\) maps to \(-3\) - \(-7\) maps to \(-7\) - \(-3\) maps to \(-3\) Since each input (domain value) is associated with a unique output (range value), the relation is indeed a function. ### Summary - **Domain**: \(\{-6, 2, -7, -3\}\) - **Range**: \(\{5, -3, -7\}\) - **Is it a function?**: Yes, it is a function.