Is this a function? \( D:-1,1,2,4 \) \( R:-2,1,3,2 \)

Yes, the given relation is a **function**. Let's break it down: ### Definitions: - **Domain (D):** The set of all possible input values. - **Range (R):** The set of all possible output values. - **Function:** A relation where each element in the domain is associated with exactly one element in the range. ### Provided Sets: - **Domain (D):** \{-1, 1, 2, 4\} - **Range (R):** \{-2, 1, 3, 2\} ### Interpretation: Assuming the elements are paired in the order they are listed, we have the following ordered pairs: - \(-1 \rightarrow -2\) - \(1 \rightarrow 1\) - \(2 \rightarrow 3\) - \(4 \rightarrow 2\) ### Verification: 1. **Uniqueness of Output:** - Each input from the domain maps to exactly one output in the range. - Note that the output "2" appears twice in the range, but this is acceptable in a function because different inputs can map to the same output. 2. **No Input Maps to Multiple Outputs:** - Every element in the domain has only one corresponding element in the range. Since every element in the domain is paired with exactly one element in the range and no input maps to multiple outputs, the relation satisfies the definition of a function. ### Conclusion: **Yes, this is a function because each element in the domain is paired with exactly one element in the range.**