Which relation is not a function?
Question 4 options:

{(–13, –10), (–15, –12), (–11, –8), (–16, 4)}

{(8, 17), (5, 5), (8, –3), (4, –1)}

{(–14, –2), (–10, 6), (–1, 3), (10, 6)}

{(0, –2), (–4, 6), (4, 15), (12, 6)}

A relation is a function if each input (the first element in each pair) is associated with exactly one output (the second element in each pair). To determine which relation is **not** a function, we check if any input is associated with more than one output.

Let's examine each relation:

1. **{(–13, –10), (–15, –12), (–11, –8), (–16, 4)}**  
   - Inputs: –13, –15, –11, –16  
   - Each input is unique, so this relation **is** a function.

2. **{(8, 17), (5, 5), (8, –3), (4, –1)}**  
   - Inputs: 8, 5, 8, 4  
   - The input 8 is associated with both 17 and –3, so this relation **is not** a function.

3. **{(–14, –2), (–10, 6), (–1, 3), (10, 6)}**  
   - Inputs: –14, –10, –1, 10  
   - Each input is unique, so this relation **is** a function.

4. **{(0, –2), (–4, 6), (4, 15), (12, 6)}**  
   - Inputs: 0, –4, 4, 12  
   - Each input is unique, so this relation **is** a function.

### Conclusion:
The second relation **{(8, 17), (5, 5), (8, –3), (4, –1)}** is **not** a function because the input 8 is mapped to two different outputs, 17 and –3.

Would you like more details or have any other questions?

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**Related Questions:**

1. What makes a relation a function in general terms?
2. Can a function have the same output for different inputs?
3. How would you graphically determine if a relation is a function?
4. What are real-life examples of functions and non-functions?
5. How does the vertical line test help in identifying functions?

**Tip:** When analyzing a relation, always check if any input has more than one corresponding output to determine if it is a function.

Understand what makes a relation a function with examples. Learn how to determine if a relation is not a function using specific examples provided by the user.

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