Let's analyze the mapping diagram to determine if it represents a function.

A relation is a function if each element in the domain (Set A) maps to exactly one element in the range (Set B). In other words, each element in Set A should have a unique output in Set B.

Analysis of Diagram:

• In Set A, we have the elements $3$, $1$, and $0$.
• The mappings are as follows:
  • $3$ maps to $4$,
  • $1$ maps to $5$,
  • $0$ maps to $7$.

Each element in Set A has only one unique mapping to an element in Set B, which means there are no elements in Set A with multiple mappings.

Conclusion: This mapping is a function because each element in Set A is associated with only one element in Set B.

Answer for the Blanks:

1. "does represent" (indicating it is a function)
2. "every element" (every element in the domain has a unique mapping)
3. "Set A" (the domain set being referred to)
4. "only one" (each element in Set A maps to only one element in Set B)

The completed answer should be:

The mapping diagram above does represent a function since every element in Set A maps to only one element in Set B.

Would you like a deeper explanation of functions and mappings?

Related Questions

1. What is the difference between a function and a general relation?
2. Can a function have multiple elements in Set A map to the same element in Set B?
3. How would the diagram look if it did not represent a function?
4. What are examples of real-world mappings that form functions?
5. Can functions have unused elements in Set B?

Tip:

When analyzing mappings, always check if any element in the domain has multiple outputs. If it does, it’s not a function!