To determine which of the given sets of ordered pairs is a function, we need to remember that a function maps each input (the first element in the ordered pairs, or the "x" value) to exactly one output (the second element in the ordered pairs, or the "y" value). In other words, no two ordered pairs should have the same first element with different second elements.

Let's analyze each set of ordered pairs:

1. Set 1:
   $\{(6, 1), (-3, 1), (3, 5), (2, 4), (-1, 2)\}$
   No two pairs share the same first element ("x" value).
   This is a function.

2. Set 2:
   $\{(1, 2), (-4, 8), (-3, 5), (1, -2), (7, 12)\}$
   The first element "1" is paired with both 2 and -2, which means it violates the definition of a function.
   This is not a function.

3. Set 3:
   $\{(5, 4), (5, 6), (5, 8), (5, 10), (5, 12)\}$
   The first element "5" is paired with multiple values (4, 6, 8, 10, and 12).
   This is not a function.

4. Set 4:
   $\{(5, 4), (4, 3), (3, 2), (4, 5), (2, 1)\}$
   The first element "4" is paired with both 3 and 5, which means it violates the definition of a function.
   This is not a function.

Conclusion:

The first set of ordered pairs is a function.

Would you like further details or clarification on any part of this explanation?

Here are five related questions:

1. What is the definition of a one-to-one function?
2. How can we determine the domain and range of a function from a set of ordered pairs?
3. What is the difference between a relation and a function in mathematics?
4. How would we express a function using a graph instead of ordered pairs?
5. Can a function have the same output (y-value) for different inputs (x-values)?

Tip: In a function, each input must be paired with exactly one output, but multiple inputs can share the same output.