To determine if each graph represents a function, we can apply the vertical line test. This test states that if any vertical line drawn through the graph touches the curve at more than one point, then the graph does not represent a function.

Let’s evaluate each graph:

1. Graph 1:

   • The vertical line at $x = 0$ intersects the graph at two points (one filled, one empty), meaning it fails the vertical line test.
   • Not a function.

2. Graph 2:

   • Every vertical line will intersect the graph at only one point.
   • It is a function.

3. Graph 3:

   • The points are scattered, and no vertical line would pass through more than one point.
   • It is a function.

4. Graph 4:

   • A vertical line at any $x$-value will only intersect the graph once.
   • It is a function.

5. Graph 5:

   • A vertical line at $x = 1$ will intersect the circle at two points, meaning it fails the vertical line test.
   • Not a function.

6. Graph 6:

   • The points are isolated, and no vertical line will intersect more than one point.
   • It is a function.

Summary:

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

Do you want further details or explanations for any of these graphs?

Related Questions:

1. How does the vertical line test help in determining if a graph is a function?
2. Can a graph with a curve that doubles back on itself represent a function?
3. Why does an isolated set of points always pass the vertical line test?
4. What are examples of real-world functions that might look like these graphs?
5. How would the horizontal line test differ from the vertical line test in terms of functions?

Tip:

Always remember, a function must assign exactly one output (y-value) for each input (x-value).