To determine whether the mapping shown represents a function, let's analyze the mapping in the diagram.

Analysis

In the mapping diagram:

• Set A contains elements $7$, $9$, and $-1$.
• Set B contains elements $8$, $2$, and $6$.

Each element in Set A has an arrow pointing to exactly one element in Set B:

• $7$ maps to $8$.
• $9$ maps to $2$.
• $-1$ maps to $2$.

Criteria for a Function

A mapping is a function if each element in the domain (Set A) maps to only one element in the range (Set B). Multiple elements in Set A can map to the same element in Set B, but one element in Set A cannot map to multiple elements in Set B.

Conclusion

Since each element in Set A has only one arrow going to an element in Set B, this mapping does represent a function.

Filling in the Blanks

The blanks in the question can be filled as follows:

1. First Blank: "is" (The mapping diagram above is a function)
2. Second Blank: "each element" (since each element in Set A)
3. Third Blank: "one" (maps to one element)
4. Fourth Blank: "Set A" (in Set A where)
5. Fifth Blank: "no element" (there is no element with more than one mapping).

Complete Answer

The mapping diagram above is a function since each element in Set A maps to one element in Set B where there is no element with more than one mapping.

Would you like further details or have any questions?

Here are five questions related to this concept:

1. What conditions must a mapping satisfy to be considered a function?
2. Can a function have multiple elements in Set A mapping to the same element in Set B?
3. What happens if one element in Set A maps to two different elements in Set B?
4. How can we visually determine if a mapping diagram represents a function?
5. What is the difference between a function and a relation in mathematics?

Tip: Always check that each input (element in Set A) maps to only one output (element in Set B) to confirm a function.