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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).

Which set of ordered pairs does not represent a function?

Learn how to identify which set of ordered pairs does not represent a function by analyzing if each input (x-value) corresponds to a single output (y-value). The problem tests the understanding of relations, ordered pairs, and functions, and is suitable for students in Grades 8-10.

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