The image shows a set of graphs with a question asking whether each graph represents a function. To determine if a graph represents a function, we can apply the vertical line test. This test states that if a vertical line intersects the graph at more than one point, then the graph does not represent a function.

Here’s the analysis for each graph based on the vertical line test:

1. Graph 1: This is a straight line. A vertical line will only intersect it once at any point. Yes, this is a function.

2. Graph 2: The graph has segments and a point above it. A vertical line would intersect the graph more than once in certain places (e.g., where the open circle and the filled circle align). No, this is not a function.

3. Graph 3: This is a V-shaped graph. A vertical line will only intersect at one point for any x-value. Yes, this is a function.

4. Graph 4: This is a circle. A vertical line will intersect the circle at two points in most places. No, this is not a function.

5. Graph 5: The graph shows a set of distinct points. A vertical line will intersect each point only once. Yes, this is a function.

6. Graph 6: This graph has points where a vertical line would intersect at more than one point (e.g., multiple points align on the same vertical line). No, this is not a function.

Summary:

1. Graph 1: Yes (function)
2. Graph 2: No (not a function)
3. Graph 3: Yes (function)
4. Graph 4: No (not a function)
5. Graph 5: Yes (function)
6. Graph 6: No (not a function)

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

Here are five related questions for further exploration:

1. What is the vertical line test and why does it work for identifying functions?
2. Can a graph be a function if it has open or closed circles on the same vertical line?
3. How do you determine if a set of points is a function just by looking at the graph?
4. What is the difference between a function and a relation in terms of graph representation?
5. Can a graph ever be a function if it is symmetric about the y-axis?

Tip: Always remember that a function assigns exactly one output (y-value) for each input (x-value), which is why the vertical line test works to identify functions.