To determine which set of ordered pairs represents a function, we must check whether each input (the first element of the ordered pair) corresponds to only one output (the second element). A function cannot have the same input associated with multiple outputs.

Let's review each set:

1. Set 1: {(8, −5), (2, 9), (5, 9), (5, −1)}

   • The input 5 is associated with two different outputs (9 and −1), so this is not a function.

2. Set 2: {(8, −7), (4, 7), (2, −6), (4, −1)}

   • The input 4 is associated with two different outputs (7 and −1), so this is not a function.

3. Set 3: {(4, 6), (−8, 4), (−7, 4), (3, 9)}

   • Each input corresponds to exactly one output. This is a function.

4. Set 4: {(−4, 0), (1, 2), (−3, −5), (1, 8)}

   • The input 1 is associated with two different outputs (2 and 8), so this is not a function.

Thus, Set 3 represents a function.

Answer: Set 3 {(4, 6), (−8, 4), (−7, 4), (3, 9)}

Do you need more details or have any questions?

Related Questions:

1. What is the definition of a function in terms of ordered pairs?
2. How can you identify if a set of ordered pairs is not a function?
3. What is the difference between a function and a relation?
4. How would you graph the ordered pairs in Set 3 to visualize the function?
5. Can a function have the same output for different inputs?

Tip: A function assigns exactly one output for every input, but different inputs can share the same output.