In the image, there are two sets of relations depicted using arrow diagrams. Let’s analyze them individually to determine which is a function and which is not.

Left Diagram:

• The left side has the following mappings:
  • $5 \to 6$
  • $5 \to 1$
  • $7 \to 9$

Explanation:

• A function requires that each input (element from the first set) is mapped to exactly one output.
• Here, the element $5$ is mapped to both $6$ and $1$, which violates the definition of a function.

Thus, the left relation is not a function because one input (5) is mapped to more than one output.

Right Diagram:

• The right side has the following mappings:
  • $1 \to 7$
  • $6 \to 7$
  • $3 \to 7$

Explanation:

• Each input (1, 6, and 3) has exactly one output (7).
• There are no inputs mapped to more than one output, satisfying the definition of a function.

Thus, the right relation is a function because each input is mapped to exactly one output.

Would you like more details on functions and relations, or any specific part of this explanation clarified?

Here are 5 related questions to explore further:

1. What is the difference between a one-to-one function and a many-to-one function?
2. Can a function have multiple inputs mapping to the same output?
3. How can we represent functions algebraically as opposed to using diagrams?
4. What are some real-world examples of relations that are not functions?
5. How does the vertical line test help determine if a relation is a function?

Tip: To check if a relation is a function, remember that no input should map to more than one output!