Let's analyze whether each of the given graphs represents a function by using the Vertical Line Test. This test states that if a vertical line intersects a graph in more than one point at any x-value, the graph does not represent a function.

Analysis of the graphs:

1. Graph 1:

   • This graph shows two horizontal lines, one open on the right and the other closed on the left.
   • If you apply the vertical line test, some vertical lines will intersect both lines at the same x-value.
   • Conclusion: This is not a function.

2. Graph 2:

   • This is a diamond-shaped graph.
   • If you apply the vertical line test, vertical lines will intersect the graph at two points in some places.
   • Conclusion: This is not a function.

3. Graph 3:

   • This is a scatter plot where all points are vertically aligned but on different horizontal levels.
   • A vertical line can pass through multiple points.
   • Conclusion: This is not a function.

4. Graph 4:

   • This appears to be a sinusoidal curve.
   • Applying the vertical line test, each vertical line touches the graph at only one point.
   • Conclusion: This is a function.

5. Graph 5:

   • This graph shows two lines meeting at a corner.
   • Applying the vertical line test, each vertical line intersects the graph at exactly one point.
   • Conclusion: This is a function.

6. Graph 6:

   • This is another scatter plot, but this time the points are scattered in a more irregular manner.
   • Some vertical lines can pass through more than one point.
   • Conclusion: This is not a function.

Summary of results:

• Graph 1: No
• Graph 2: No
• Graph 3: No
• Graph 4: Yes
• Graph 5: Yes
• Graph 6: No

Would you like any further details or explanations?

Here are 5 questions to expand on this:

1. What is the Vertical Line Test, and how does it help identify functions?
2. Can a graph represent more than one function?
3. How do piecewise functions differ from those shown in Graph 5?
4. Could a curve that touches a vertical line at only one point be a function?
5. What is the difference between discrete and continuous functions?

Tip: When in doubt whether a graph represents a function, always check for the vertical line test!