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Let's analyze the six graphs to determine whether they represent functions based on the vertical line test. A graph represents a function if no vertical line crosses the graph more than once.

1. **Graph 1**: The shape is a diamond. If you draw a vertical line, it will intersect the shape at two points for most x-values.  
   - **Conclusion**: This is **not a function**.

2. **Graph 2**: This graph is a scatter plot of distinct points. Since no vertical line would pass through more than one point at a time, this satisfies the function criteria.
   - **Conclusion**: This **is a function**.

3. **Graph 3**: Another scatter plot with some points sharing the same x-coordinate (at least two points on x = 1, for example). A vertical line would pass through multiple points at certain x-values.
   - **Conclusion**: This is **not a function**.

4. **Graph 4**: A combination of open and closed points on a horizontal line. Since each x-value corresponds to at most one y-value (no overlap in the x-direction), this satisfies the criteria for a function.
   - **Conclusion**: This **is a function**.

5. **Graph 5**: This graph is a "V" shape, which passes the vertical line test as each vertical line intersects it at only one point.
   - **Conclusion**: This **is a function**.

6. **Graph 6**: The graph is a sideways parabola. A vertical line will intersect the graph at two points for certain x-values, which violates the function condition.
   - **Conclusion**: This is **not a function**.

### Summary:
- **Graph 1**: No
- **Graph 2**: Yes
- **Graph 3**: No
- **Graph 4**: Yes
- **Graph 5**: Yes
- **Graph 6**: No

Would you like further details on any of these conclusions or explanations?

Here are some related questions to expand on this:
1. How does the vertical line test work mathematically?
2. Can a scatter plot always represent a function?
3. Why is the "V" shape in Graph 5 considered a function?
4. What are other ways to identify functions besides the vertical line test?
5. Could there be cases where a graph fails the vertical line test but is still considered a function?

**Tip**: A quick way to verify if a graph is a function is to think of it as assigning a unique y-value to each x-value. If this assignment is not unique, it’s not a function!

For each graph below, state whether it represents a function.

Explore six different graphs and determine whether each one represents a function based on the vertical line test. This problem covers key concepts of functions, graphs, and how to apply the vertical line test for analysis. Suitable for students in Grades 7-10.

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