To determine which of the given sets of ordered pairs is a function, we must ensure that no two pairs have the same first coordinate (input) associated with different second coordinates (outputs). This is because a function maps each input to exactly one output.

Let's analyze each set:

1. Set: {(−8, 1), (−5, −5), (4, 1), (−7, −4)}

• First coordinates: −8, −5, 4, −7
• Each first coordinate is unique.
• This set is a function.

---

2. Set: {(9, 2), (−3, 0), (9, −8), (0, −6)}

• First coordinates: 9, −3, 9, 0
• The first coordinate 9 appears twice, with different outputs (2 and −8).
• This set is NOT a function.

---

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

• First coordinates: 8, −4, 0, 8
• The first coordinate 8 appears twice, with different outputs (0 and −3).
• This set is NOT a function.

---

4. Set: {(0, −4), (−4, −6), (−6, 2), (0, 7)}

• First coordinates: 0, −4, −6, 0
• The first coordinate 0 appears twice, with different outputs (−4 and 7).
• This set is NOT a function.

---

Final Answer:

The only set that represents a function is Set 1: {(−8, 1), (−5, −5), (4, 1), (−7, −4)}.

---

Do you want further details or clarification?
Here are 5 follow-up questions to expand your understanding:

1. What is the definition of a function in mathematics?
2. How can you identify a function from a graph instead of ordered pairs?
3. Can a function have repeated second coordinates (outputs)? Why or why not?
4. How do vertical line tests relate to determining functions?
5. What are examples of real-world scenarios where functions are applicable?

Tip: To test for a function, always ensure every input has one and only one output!