To determine if the mapping represents a function, let's examine the criteria for a function: each element in the domain (Set A) should map to exactly one element in the codomain (Set B).

Analysis of the Mapping Diagram

1. Elements in Set A:

   • 4 maps to 7.
   • 9 maps to 5.
   • -2 maps to both -4 and 5.

2. Criteria for a Function:

   • A relation is a function if each element in the domain (Set A) has a single, unique mapping to an element in the codomain (Set B).
   • Here, the element -2 in Set A maps to both -4 and 5 in Set B. This means that -2 has more than one mapping, which violates the definition of a function.

Conclusion

The mapping diagram does not represent a function because there is an element in Set A (namely, -2) that maps to more than one element in Set B.

Suggested Answers for the Fill-in-the-Blanks

• The mapping diagram above does not represent a function since there is an element in Set A where there are multiple mappings.

Would you like further details or explanations?

Here are some related questions for deeper understanding:

1. What defines a function in terms of mappings between two sets?
2. How would the mapping need to change to qualify as a function?
3. Can a function have multiple elements in Set A map to the same element in Set B?
4. What is the difference between a relation and a function?
5. How can we visually identify a function in a mapping diagram?

Tip: In a mapping diagram, check if any single element in the domain (Set A) points to more than one element in the codomain (Set B) to determine if it’s not a function.