7. Which relation is a finction? A. \( (2,7,(4,5)(4,4)(2,3),(2,1) \) B. \( (1,1)(2,2 \lambda(2,3)(4,4)(5,8) \) C. \( (2,-3)(2,3)(4,-2)(4,2)(40) \) D \( (1,0)(2,0)(1,1),(2,1)(1,3) \)

To determine which relation is a function, we need to recall the definition of a **function**: A **function** is a relation in which each input (the first element of each ordered pair) is related to exactly one output (the second element of each ordered pair). In other words, no input value is associated with more than one output value. Let's analyze each option: ### **Option A:** \[ (2,7), (4,5), (4,4), (2,3), (2,1) \] - **Input `2`** is related to **7**, **3**, and **1**. - **Input `4`** is related to **5** and **4**. **Conclusion:** Not a function (inputs have multiple outputs). --- ### **Option B:** \[ (1,1), (2,2), (2,3), (4,4), (5,8) \] - **Input `1`** is related to **1**. - **Input `2`** is related to **2** and **3**. - **Input `4`** is related to **4**. - **Input `5`** is related to **8**. **Conclusion:** Not a function (input `2` has multiple outputs). --- ### **Option C:** \[ (2,-3), (2,3), (4,-2), (4,2), (4,0) \] - **Input `2`** is related to **-3** and **3**. - **Input `4`** is related to **-2**, **2**, and **0**. **Conclusion:** Not a function (inputs have multiple outputs). --- ### **Option D:** \[ (1,0), (2,0), (1,1), (2,1), (1,3) \] - **Input `1`** is related to **0**, **1**, and **3**. - **Input `2`** is related to **0** and **1**. **Conclusion:** Not a function (inputs have multiple outputs). --- ### **Final Determination:** All the provided options contain inputs that are associated with multiple outputs, which means **none of the relations** listed is a function. **Answer:** **None of the given relations is a function.**