In the image, a mapping diagram shows the relationship between Set A and Set B. In Set A, we have values $8$, $7$, and $0$, and in Set B, we have values $4$, $-1$, and $-3$. Let's analyze the mapping:

• The number 8 from Set A is mapped to both $4$ and $-1$ in Set B.
• The number 7 from Set A is mapped to $-1$ in Set B.
• The number 0 from Set A is mapped to $-3$ in Set B.

For this mapping to represent a function, each element in Set A must map to exactly one element in Set B. However, the element 8 is mapped to two different values (both 4 and $-1$), which violates the definition of a function.

Conclusion:

The diagram does not represent a function, since the element 8 in Set A maps to two different values in Set B.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. What are the main conditions for a mapping to represent a function?
2. Can a function have more than one input map to the same output?
3. How does this mapping relate to the concept of "one-to-one" functions?
4. What would the inverse of a function look like if it exists?
5. How would the mapping change if we removed one of the connections from 8?

Tip: A function cannot have one input assigned to more than one output, but multiple inputs can share the same output.