To determine which set of ordered pairs does not represent a function, we need to check whether each input (or "x-value") corresponds to exactly one output (or "y-value"). In a function, no two ordered pairs can have the same x-value with different y-values.

Let's analyze each option:

1. Set 1: $\{(4, 0), (8, -8), (4, 1), (5, 8)\}$

   • Notice that the x-value $4$ appears twice: in $(4, 0)$ and $(4, 1)$, with different y-values. This means that this set does not represent a function.

2. Set 2: $\{(0, -9), (-6, -6), (5, 0), (2, 0)\}$

   • Every x-value is unique, so this is a function.

3. Set 3: $\{(9, 7), (8, 1), (1, -4), (-6, 2)\}$

   • Every x-value is unique, so this is a function.

4. Set 4: $\{(9, 7), (-3, 2), (6, 0), (-9, 2)\}$

   • Every x-value is unique, so this is a function.

Conclusion:

The first set, $\{(4, 0), (8, -8), (4, 1), (5, 8)\}$, does not represent a function because the x-value $4$ is repeated with different y-values.

Do you need further clarification on any of these sets?

Here are five related questions to deepen your understanding:

1. How can you determine if a graph represents a function?
2. What is the vertical line test for functions?
3. Can a function have the same y-value for different x-values?
4. What is the definition of a one-to-one function?
5. How are functions represented in real-world applications?

Tip: In functions, always ensure that each input (x-value) has a single output (y-value).