To determine whether each graph represents a function, we can use the vertical line test. If a vertical line intersects the graph at more than one point anywhere, the graph does not represent a function.

Let's analyze each graph:

1. Graph 1:

   • A vertical line at any point will only intersect the graph once.
   • Result: Yes, this is a function.

2. Graph 2:

   • A vertical line at the peak or base of the triangle will intersect the graph twice.
   • Result: No, this is not a function.

3. Graph 3:

   • A vertical line at the widest part of the ellipse intersects the graph at two points.
   • Result: No, this is not a function.

4. Graph 4:

   • A vertical line anywhere will only intersect the graph once.
   • Result: Yes, this is a function.

5. Graph 5:

   • A vertical line at several points (e.g., x = 1) will intersect the graph more than once.
   • Result: No, this is not a function.

6. Graph 6:

   • A vertical line at x = 0 intersects the graph at three points.
   • Result: No, this is not a function.

Summary:

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

Would you like more details about any specific graph or concept?

Related Questions:

1. What is the vertical line test, and why does it work to determine if a graph is a function?
2. Can you explain the difference between a relation and a function?
3. How can you identify functions algebraically?
4. What are some examples of common functions and their graphs?
5. How do you determine the domain and range of a function from a graph?

Tip:

Remember that functions have a unique output for each input. If any input maps to more than one output, it's not a function!