A set of ordered pairs represents a function if every input (first element) maps to exactly one output (second element). In other words, no two ordered pairs should have the same first element with different second elements.

Let’s check each option:

1. {(−5,−7),(−1,4),(−3,4),(5,2)}

   • Inputs: −5, −1, −3, 5
   • No repeated inputs → This is a function.

2. {(−8,−7),(4,7),(4,−9),(5,−6)}

   • Inputs: −8, 4, 4, 5
   • The input "4" is associated with two different outputs (7 and −9).
   • This is not a function.

3. {(−5,−7),(−6,7),(−1,−9),(9,7)}

   • Inputs: −5, −6, −1, 9
   • No repeated inputs → This is a function.

4. {(4,5),(1,5),(3,−7),(7,6)}

   • Inputs: 4, 1, 3, 7
   • No repeated inputs → This is a function.

Answer: The second set {(−8,−7),(4,7),(4,−9),(5,−6)} does not represent a function.

Would you like more details or have any questions?

Here are some related questions to explore:

1. How do you determine if a set of ordered pairs is a function?
2. What is the vertical line test in determining if a relation is a function?
3. Can a function have the same output for different inputs?
4. What are one-to-one functions, and how do they differ from general functions?
5. How can functions be represented other than with ordered pairs?

Tip: In any function, every input must have exactly one output. Always check for repeated inputs with different outputs when verifying if a relation is a function.