To determine whether each graph represents a function, we 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 analyze each graph:

1. Graph 1 (Line):

   • This is a straight diagonal line.
   • Passes the vertical line test, so it represents a function.
   • Answer: Yes.

2. Graph 2 (Discrete Horizontal Segments):

   • There are two horizontal line segments, one of which has an open circle at the end.
   • Passes the vertical line test, as no vertical line intersects both parts of the graph simultaneously.
   • Answer: Yes.

3. Graph 3 (V-shape):

   • This graph forms a "V" shape.
   • Fails the vertical line test, since a vertical line through the vertex of the "V" will intersect the graph at two points.
   • Answer: No.

4. Graph 4 (Circle):

   • This is a full circle.
   • Fails the vertical line test, as a vertical line through the center will intersect the circle at two points.
   • Answer: No.

5. Graph 5 (Discrete Points):

   • There are several points plotted, but none are vertically aligned.
   • Passes the vertical line test, since no vertical line intersects more than one point.
   • Answer: Yes.

6. Graph 6 (Discrete Points with vertical alignment):

   • There are two points on the same vertical line.
   • Fails the vertical line test, since a vertical line through these points would intersect both points.
   • Answer: No.

Summary of Answers:

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

Let me know if you need more details or have any questions!

Here are 5 questions to expand your understanding:

1. What is the vertical line test, and how does it apply to different types of graphs?
2. Why does a circle fail the vertical line test, even though each x-value has two corresponding y-values?
3. How do discrete points differ from continuous lines in terms of representing functions?
4. Can a graph with open circles at certain points still represent a function?
5. How does symmetry about the y-axis affect whether a graph represents a function?

Tip: The vertical line test is a quick and reliable way to determine if a graph represents a function—just check if a vertical line crosses more than one point!