The image shows a mapping diagram with two sets:

• Set A: {5, 8, -2}
• Set B: {7, -4, 4}

The mapping is as follows:

• 5 maps to 7.
• 8 maps to -4.
• -2 maps to 4.

To determine if this mapping represents a function, recall the definition of a function:

• A relation is a function if each element in Set A (the domain) is mapped to exactly one element in Set B (the range). This means that no element in Set A should map to more than one element in Set B.

Answering the Blanks:

• The mapping diagram above does represent a function since each element in Set A maps to exactly one element in Set B where there is no element in Set A that maps to more than one element in Set B.

Thus, the relation is a function because each element from Set A has a unique mapping to a single element in Set B.

Would you like further details on this explanation, or do you have any questions?

Here are 5 related questions to consider:

1. What would make the diagram not represent a function?
2. How does the definition of a function differ from that of a relation?
3. What happens if two different elements in Set A map to the same element in Set B?
4. Can a function be one-to-one if two elements in Set A map to the same element in Set B?
5. What is the difference between the domain and the range in this context?

Tip: Always check if any element in the domain (Set A) maps to more than one element in the range to verify if a relation is a function.