A function is defined as a relation where each input (x-coordinate) has exactly one output (y-coordinate). This means that no x-coordinate can be repeated in the set of ordered pairs.

Let's analyze the given graphs:

1. First set of points: $(-2, 3), (-1, 2), (1, 1), (2, -1), (2, -3), (4, -5)$ Here, the x-coordinate 2 is repeated, which means there are two different y-values for x = 2, namely -1 and -3. This violates the definition of a function.

2. Second set of points: $(-4, -4), (-2, 2), (1, 1), (2, -5), (4, -3), (4, 4)$ The x-coordinate 4 is repeated, with y-values -3 and 4. This also violates the definition of a function.

3. Third set of points: $(-3, 2), (-2, 2), (0, 1), (1, 3), (2, -4), (4, -1)$ All x-coordinates are unique, so this set represents a function.

4. Fourth set of points: $(-4, 2), (-2, 1), (-2, -1), (0, -2), (0, -4), (2, -5)$ The x-coordinates -2 and 0 are repeated with different y-values. This violates the definition of a function.

Conclusion: The third graph shows a set of ordered pairs that represent a function.

Would you like more details on why this is the case? Or do you have any further questions?

Additional questions:

1. What happens if an x-coordinate is repeated with the same y-value?
2. How can you graph a function based on its ordered pairs?
3. What is the vertical line test, and how does it help in identifying functions from graphs?
4. Can a function have more than one output for a single input in any case?
5. How do you differentiate between a function and a relation?

Tip: To check if a set of ordered pairs represents a function, make sure that no x-coordinate is repeated with a different y-coordinate.