Does this set of ordered pairs respect a function? Why or why not?

Yes, the set of ordered pairs \(\{(-1, 5), (0, -3), (2, 7), (4, 0), (7, 5)\}\) does represent a function.

A set of ordered pairs defines a function if each input (the first element of the pair, known as the domain) is associated with exactly one output (the second element of the pair, known as the range). This means that no two pairs can have the same first element with different second elements.

In this set:
- The inputs are: -1, 0, 2, 4, and 7.
- Each of these inputs is unique and there are no repetitions.

Since every input is paired with exactly one output, this set of ordered pairs respects the definition of a function.