Functions \( 1 \leftarrow \quad \) State the domain and range for the following relation. Then determine whether the relation represents a function. \( \{(5,4),(-2,4),(7,5),(5,13)\} \) Part 1 of 3

Sure! Let's break down the problem step by step. ### Given Relation: \[ \{(5, 4),\ (-2, 4),\ (7, 5),\ (5, 13)\} \] ### 1. **Domain** The **domain** of a relation consists of all the **first elements** (inputs) in each ordered pair. - **First elements**: \(5, -2, 7, 5\) Since sets do not include duplicate elements, we list each unique input once. - **Domain**: \(\{ -2,\ 5,\ 7 \}\) ### 2. **Range** The **range** of a relation consists of all the **second elements** (outputs) in each ordered pair. - **Second elements**: \(4, 4, 5, 13\) Again, listing each unique output once. - **Range**: \(\{ 4,\ 5,\ 13 \}\) ### 3. **Determining if the Relation is a Function** A **function** is a special type of relation where **each input is associated with exactly one output**. In other words, no two ordered pairs should have the same first element paired with different second elements. Let's examine the given relation: - \(5\) is paired with **4** in \((5, 4)\) - \(5\) is also paired with **13** in \((5, 13)\) Here, the input \(5\) is associated with **two different outputs** (\(4\) and \(13\)). This violates the definition of a function. - **Conclusion**: The relation **does not** represent a function. ### **Summary** - **Domain**: \(\{ -2,\ 5,\ 7 \}\) - **Range**: \(\{ 4,\ 5,\ 13 \}\) - **Is it a function?**: **No**, because the input \(5\) corresponds to multiple outputs.