A function is a relation where each input (first component of the ordered pair, often called the "domain") is related to exactly one output (second component of the ordered pair, often called the "range"). In other words, for a set of ordered pairs to represent a function, no two different ordered pairs can have the same first component (input).

Let's analyze the options:

1. {(−1,−5), (5,7), (−3,4), (−3,9)}
   The input $-3$ is repeated with two different outputs: 4 and 9. This means this set does not represent a function.

2. {(−9,−6), (1,5), (−1,3), (5,5)}
   All inputs are unique. This set does represent a function.

3. {(2,−5), (−9,9), (6,0), (3,9)}
   All inputs are unique. This set does represent a function.

4. {(4,0), (2,−6), (5,0), (0,5)}
   All inputs are unique. This set does represent a function.

Answer:

The set of ordered pairs that does not represent a function is: {(−1,−5), (5,7), (−3,4), (−3,9)}

Would you like a further explanation of how functions are defined?

Here are some related questions:

1. What are the key differences between functions and relations?
2. How can you tell if a graph represents a function?
3. What is the vertical line test, and how does it work?
4. Can a function have two identical outputs for different inputs?
5. What are some real-world examples of functions?

Tip: Always check that every input has only one output when determining if a set of ordered pairs is a function!