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.