https://file.aiquickdraw.com/mathbot/file/17285608550968t40nzfc.jpg

To determine whether each graph represents a function, we can apply the **Vertical Line Test**. A graph represents a function if and only if no vertical line intersects the graph at more than one point. Let’s go through each graph:

1. **Graph 1**: There are several dots in different vertical positions, and no vertical line passes through more than one dot. 
   - **Answer**: Yes, this is a function.

2. **Graph 2**: This graph appears to be a triangle. If you draw a vertical line through the graph, it will intersect the triangle at more than one point in some places (especially near the top).
   - **Answer**: No, this is not a function.

3. **Graph 3**: Similar to Graph 1, it contains several points, but some vertical lines would pass through two points (around \(x = 2\)).
   - **Answer**: No, this is not a function.

4. **Graph 4**: This graph has dots and some open circles. However, each vertical line intersects only one point or an open circle.
   - **Answer**: Yes, this is a function.

5. **Graph 5**: This is a parabola, which passes the vertical line test since each vertical line intersects the curve at only one point.
   - **Answer**: Yes, this is a function.

6. **Graph 6**: This graph appears to be made of two lines joined at a point, and no vertical line intersects it at more than one point.
   - **Answer**: Yes, this is a function.

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

Would you like more details on any of the graphs or clarification? 

Here are five questions that expand on this topic:
1. What is the vertical line test, and how is it used?
2. Can a graph with isolated points (like Graph 1) always be considered a function?
3. How do open and closed circles affect whether a graph is a function?
4. What are the different types of functions represented by curves like parabolas?
5. How can we identify piecewise functions graphically?

**Tip**: For complex graphs, always check each part of the graph carefully when applying the vertical line test.

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

Learn how to determine if a graph represents a function by applying the Vertical Line Test. This problem helps students identify functions by analyzing graphs with points, curves, and lines. Suitable for students in Grades 8-10.

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