The question asks us to determine whether the mapping shown represents a function. Let’s analyze the diagram carefully.

Key observations:

1. Definition of a function: A mapping is a function if every element in the domain (Set A) is mapped to exactly one element in the codomain (Set B). In simpler terms:

   • Each input must have only one output.
   • Multiple inputs can map to the same output, but a single input cannot map to multiple outputs.

2. Mapping details:

   • From Set A:
     • $-4 \mapsto 0$
     • $4 \mapsto 2$
     • $-3 \mapsto -1$
     • $5 \mapsto 1$
   • All inputs from Set A have exactly one output in Set B.

3. Conclusion: Since each element in Set A is mapped to exactly one element in Set B, this mapping represents a function.

Fill-in-the-blanks solution:

The mapping diagram above represents a function since each input in Set A has exactly one output in Set B.

Would you like further clarification or a deeper explanation of functions and mappings? Let me know!

Related questions:

1. What are the key differences between a function and a relation?
2. Can a function have elements in the codomain that are not mapped by the domain?
3. How can you tell if a mapping is not a function just by looking at the diagram?
4. What is the difference between injective, surjective, and bijective functions?
5. Can a function map multiple domain elements to the same codomain element?

Tip:

When analyzing functions, always check that no single input (from the domain) maps to multiple outputs (in the codomain).