The question is asking whether the given mapping diagram represents a function.

In mathematics, a mapping (or relation) is considered a function if every element in the domain (Set A) is mapped to exactly one element in the codomain (Set B). In other words, each element of Set A should point to only one value in Set B for it to qualify as a function.

Analyzing the Diagram:

1. Elements in Set A: {-4, 4, -1, 5}
2. Elements in Set B: {6, 0, 7}
3. Mappings:
   • -4 maps to 6
   • 4 maps to 0
   • -1 maps to 0
   • 5 maps to 7

From this, we observe that:

• Each element in Set A has only one corresponding element in Set B.
• No element in Set A is mapped to more than one element in Set B.

Therefore, this mapping does represent a function.

Filling in the Blanks

The correct response would be:

• "The mapping diagram above represents a function since each element in Set A is mapped to only one element in Set B."

Would you like more details or have any questions on this explanation?

Here are five questions to further explore this concept:

1. What are the criteria for determining if a mapping is not a function?
2. Can a function map multiple elements from the domain to the same element in the codomain?
3. How does a one-to-one function differ from a regular function?
4. What is the difference between a function and a relation in terms of mappings?
5. How can we represent functions using graphs instead of mapping diagrams?

Tip: Always remember that a function assigns exactly one output to each input; no input can have more than one output in a valid function.