https://file.aiquickdraw.com/mathbot/file/1727076163341iun1icxe.jpg

The image you uploaded shows a diagram representing a mapping \( f: A \to B \) between two sets. There are two sets labeled \( A \) and \( B \), and the elements of set \( A \) (on the left) are mapped to the elements of set \( B \) (on the right). Based on the provided diagram, I can help analyze the domain and range.

### Key components:
- **Domain** refers to the set of input values (elements from set \( A \)).
- **Range** refers to the set of output values (elements from set \( B \)) that are actually used in the mapping (not necessarily all elements of \( B \)).

To determine which of the provided options (A, B, C, D) gives the correct domain and range, let's break down the sets:

1. **Domain** is the entire set \( A \), which appears to be \( \{a, b, c\} \).
2. **Range** will be the set of elements in \( B \) that are mapped to by elements of \( A \). From the diagram, it seems like elements of \( A \) are mapped to either \( 2 \) or \( 3 \), so the range is \( \{2, 3\} \).

### Now let's check the options:

- **a.** Domain = \( \{a, b, c\} \), Range = \( \{2, 3\} \) (this is the correct option based on the analysis)
- **b.** Domain = \( \{a, b, c\} \), Range = \( \{1, 4\} \) (incorrect range)
- **c.** Domain = \( \{a, b, c\} \), Range = \( \{1, 2, 3, 4\} \) (incorrect range)
- **d.** Domain = \( \{1, 2, 3, 4\} \), Range = \( \{2, 3\} \) (incorrect domain)

### Conclusion:
The correct answer is **Option A**: Domain = \( \{a, b, c\} \), Range = \( \{2, 3\} \).

Would you like more details or have any other questions?

Here are 5 related questions to deepen understanding:
1. How do you determine the domain and range in a function diagram?
2. What is the difference between range and codomain in a mapping?
3. How can we verify if a mapping is a function?
4. What is an injective (one-to-one) function in the context of mappings?
5. How would the diagram change if an element in \( A \) was mapped to multiple elements in \( B \)?

**Tip**: Always check if each element in the domain maps to exactly one element in the range to ensure it’s a valid function.

Given a mapping f: A → B, determine the domain and range based on the diagram provided.

This question involves analyzing a function mapping diagram where elements from set A are mapped to set B. The problem asks to identify the correct domain and range, focusing on the concepts of input-output relationships. Suitable for students in Grades 8-10.

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