In order for a set of ordered pairs to represent a function, each input (the x-coordinate) must correspond to exactly one output (the y-coordinate). This means that no two ordered pairs can have the same first element (input) with different second elements (outputs).

Let’s analyze each option:

1. {(4,3), (−5,−5), (4,6), (−2,8)}

   • The input 4 appears twice with different outputs: (4, 3) and (4, 6).
   • This set does not represent a function.

2. {(0,−8), (−7,3), (−2,9), (−7,−9)}

   • The input −7 appears twice with different outputs: (−7, 3) and (−7, −9).
   • This set does not represent a function.

3. {(−5,5), (−9,−2), (−1,5), (3,−9)}

   • Each input has a unique output.
   • This set represents a function.

4. {(0,1), (−8,−5), (9,7), (9,−5)}

   • The input 9 appears twice with different outputs: (9, 7) and (9, −5).
   • This set does not represent a function.

Correct Answer:

The set of ordered pairs that represents a function is {(−5,5), (−9,−2), (−1,5), (3,−9)}.

Would you like more details or have any other questions?

Here are some related questions for further practice:

1. What is the definition of a function in mathematics?
2. How can you tell if a set of points on a graph represents a function?
3. Can a function have two different y-values for the same x-value?
4. What is the vertical line test and how does it relate to functions?
5. How do you find the domain and range of a function?

Tip: When checking if a set of ordered pairs represents a function, focus on ensuring that no x-value repeats with different y-values.