Based on the uploaded image, I can help analyze the mathematical content and provide solutions. Here's an analysis and breakdown:

1. Function Determination (Diagram with Arrows)

In the first question about mapping diagrams:

• A function assigns exactly one output for each input.
• If the same input has multiple outputs, it is not a function.

From the diagram:

• Input "1" has three outputs (2, 3, 4). This violates the definition of a function.
• Answer: No, it is not a function.

2. Table Representation

In the second question regarding the table:

• A function must have unique y values for each x value.

In the given table:

• The x values (-3, -2, -1, 1, 6) map to distinct y values (8, 5, 8, 4, 6).
• Although y = 8 repeats, it is valid because different x values are associated with it.
• Answer: Yes, it represents a function.

3. Custom Function Example

You are asked to create a table representing a function. Here's an example:

This satisfies the function definition because each x has a unique y.

4. Mapping Diagram that is Not a Function

You can create a mapping diagram where one input maps to multiple outputs. For example:

• Input "7" connects to outputs "8" and "9".
• Input "6" connects to output "8".

This violates the function rule as one input connects to more than one output.

Would you like further explanations or examples? Let me know! Here are 5 related questions:

1. How do we determine if a relation is a function in general?
2. Can a function have repeated y values for different x values? Why?
3. How can you graphically verify if a relation is a function?
4. What are real-life examples of functions and non-functions?
5. Why is the vertical line test important for functions?

Tip: Always check if any input corresponds to more than one output to verify if a relation is a function.