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To determine which set of ordered pairs represents a function, we need to check if each input (or \(x\)-coordinate) corresponds to only one output (or \(y\)-coordinate). In other words, no \(x\)-value should be repeated with different \(y\)-values.

Let's analyze each option:

1. **\(\{(-4, -7), (8, 7), (8, 2), (-8, -4)\}\):**
   - The \(x\)-value 8 appears twice with different \(y\)-values (7 and 2).
   - This set does **not** represent a function.

2. **\(\{(7, 6), (-1, 8), (-8, 0), (-1, -2)\}\):**
   - The \(x\)-value \(-1\) appears twice with different \(y\)-values (8 and -2).
   - This set does **not** represent a function.

3. **\(\{(2, 8), (-4, 1), (5, 0), (-8, 1)\}\):**
   - All \(x\)-values are unique.
   - This set **does** represent a function.

4. **\(\{(2, 4), (2, -8), (-5, 0), (4, -6)\}\):**
   - The \(x\)-value 2 appears twice with different \(y\)-values (4 and -8).
   - This set does **not** represent a function.

### Correct Answer:
The set \(\{(2, 8), (-4, 1), (5, 0), (-8, 1)\}\) (option 3) represents a function.

Would you like any more details or have any questions?

### Related Questions:
1. What defines a relation as a function?
2. Can a function have the same \(y\)-value for different \(x\)-values?
3. How can the vertical line test be used to identify functions on a graph?
4. What is the difference between a one-to-one function and a many-to-one function?
5. How do you express a function algebraically instead of using ordered pairs?

### Tip:
A quick way to verify if a set represents a function is to ensure that no \(x\)-value appears more than once with different \(y\)-values!

Which set of ordered pairs represents a function?

Determine which set of ordered pairs represents a function. Understand how to identify functions by ensuring no x-value repeats with different y-values. Ideal for Grades 7-10 students learning about functions and relations.

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