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

Let's analyze each option:

1. {(8,5), (−2,3), (−8,5), (−8,9)}

   • The pairs $(-8, 5)$ and $(-8, 9)$ have the same first element, $-8$, but different second elements (5 and 9).
   • This is not a function.

2. {(1,4), (−6,1), (1,−9), (2,−7)}

   • The pairs $(1, 4)$ and $(1, −9)$ have the same first element, $1$, but different second elements (4 and -9).
   • This is not a function.

3. {(−8,8), (−6,3), (−7,−9), (−2,−9)}

   • All first elements are unique: $-8$, $-6$, $-7$, and $-2$.
   • This is a function.

4. {(−3,0), (6,7), (−3,−8), (−1,5)}

   • The pairs $(-3, 0)$ and $(-3, −8)$ have the same first element, $-3$, but different second elements (0 and -8).
   • This is not a function.

The correct answer is Option 3: {(-8,8), (-6,3), (-7,-9), (-2,-9)}.

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:

1. What is the definition of a function in mathematics?
2. How can you determine if a graph represents a function?
3. What is the difference between a function and a relation?
4. Can a function have more than one output for the same input?
5. How do you identify the domain and range of a function?

Tip: When checking if a set of ordered pairs represents a function, always verify that each input (first element) is paired with only one output (second element).