https://file.aiquickdraw.com/mathbot/file/1730934160974bjc2wde1.jpg

To determine if each relation is a function, we need to examine whether each input (first element in each ordered pair) has a unique output (second element in each ordered pair). If an input has more than one output, it is not a function. Let's go through each relation provided in the image:

1. **Relation \(\{(2, 2), (4, 4), (6, 6), (8, 8)\}\):**
   - Each input (2, 4, 6, 8) is associated with a unique output.
   - **This is a function.**

2. **Relation \(\{(0, 3), (3, 5), (5, 6), (8, 4)\}\):**
   - Each input (0, 3, 5, 8) is associated with a unique output.
   - **This is a function.**

3. **Relation \(\{(1, 2), (3, 3), (4, 8), (6, 3)\}\):**
   - Each input (1, 3, 4, 6) is associated with a unique output.
   - **This is a function.**

4. **Relation \(\{(3, 4), (5, 2), (5, 6), (7, 3)\}\):**
   - The input 5 is associated with two different outputs (2 and 6).
   - **This is not a function.**

Based on this analysis, the correct classification is:

- **First Relation:** Function
- **Second Relation:** Function
- **Third Relation:** Function
- **Fourth Relation:** Not a Function

It seems like the answers selected in the image are correct.

Would you like more details or have any questions about functions?

Here are some related questions to expand understanding:
1. How can you determine if a set of points on a graph represents a function?
2. What is the vertical line test, and how does it relate to functions?
3. Can a function have the same output for multiple inputs? Why or why not?
4. How are functions applied in real-world scenarios?
5. What is the difference between a function and a relation?

**Tip:** Always check for duplicate inputs with different outputs when determining if a relation is a function.

Select if each given relation is a function or not.

Learn how to identify if each relation is a function. This problem helps in understanding the concept of functions by examining whether each input has a unique output in a set of ordered pairs. Suitable for students in Grades 9-10.

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