To determine which of the provided sets of ordered pairs is not a one-to-one function, we need to recall the definition of a one-to-one function (also called an injective function). A function is one-to-one if no two different elements in the domain map to the same element in the range.

Let's examine each set:

1. First option:
   $\{ (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4) \}$
   In this set, we see that both $(-2, 4)$ and $(2, 4)$ map to the same value (4), and both $(-1, 1)$ and $(1, 1)$ map to the same value (1).
   This is not a one-to-one function because multiple inputs (domain values) map to the same output (range values).

2. Second option:
   $\{ (-6, 2), (-3, 1), (0, 0) \}$
   Here, each input maps to a distinct output, so this is a one-to-one function.

3. Third option:
   $\{ (-5, 4), (-3, 2), (-1, 0) \}$
   Each input has a unique output, so this is a one-to-one function.

4. Fourth option:
   $\{ (5, 7) \}$
   This set contains only one element, so by default, it is a one-to-one function.

Conclusion:

The first option is not a one-to-one function. Therefore, the answer is the first option.

Would you like further explanation or details? Here are some additional questions you might find helpful:

1. What is the formal definition of a one-to-one function?
2. Can a function be one-to-one if there is only one element in the set?
3. How does a one-to-one function differ from a many-to-one function?
4. What is an example of a real-world one-to-one function?
5. How can you check if a graph represents a one-to-one function?

Tip: When analyzing one-to-one functions, always check if different domain values map to the same range value.