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.