https://file.aiquickdraw.com/mathbot/file/17303517075240c7gg22d.jpg

To solve this question, let’s analyze each part (a, b, and c) in terms of whether it represents a function, and if so, identify the domain, codomain, and the rule of the function.

### Definitions:
1. **Function**: A relation where each element in the domain is associated with exactly one element in the codomain.
2. **Domain**: The set of inputs (values in set \( A \)).
3. **Codomain**: The set of possible outputs (values in set \( B \)).

### Analysis:
- **Diagram a**:
  - Elements in \( A \): \{-2, -1, 0, 1\}
  - Elements in \( B \): \{0, 1, 4, 9\}
  - Observations: \( -2 \) in \( A \) maps to both \( 1 \) and \( 9 \), which means that there is more than one output for a single input.
  - **Conclusion**: Not a function (because each element in \( A \) does not map to a unique element in \( B \)).

- **Diagram b**:
  - Elements in \( A \): \{1, 2, 3\}
  - Elements in \( B \): \{1, 2, 3, 4\}
  - Observations: Each element in \( A \) maps to a unique element in \( B \).
  - **Conclusion**: This is a function.
  - **Domain**: \{1, 2, 3\}
  - **Codomain**: \{1, 2, 3, 4\}
  - **Rule**: Based on the mapping, the function appears to follow \( f(x) = x \).

- **Diagram c**:
  - Elements in \( A \): \{-1, 0, 1, 2\}
  - Elements in \( B \): \{3\}
  - Observations: Each element in \( A \) maps to the same element (3) in \( B \).
  - **Conclusion**: This is a function.
  - **Domain**: \{-1, 0, 1, 2\}
  - **Codomain**: \{3\}
  - **Rule**: The function maps every element in \( A \) to 3, so the rule can be written as \( f(x) = 3 \).

### Summary:
- **Diagram a**: Not a function.
- **Diagram b**: Function with domain \{1, 2, 3\}, codomain \{1, 2, 3, 4\}, rule \( f(x) = x \).
- **Diagram c**: Function with domain \{-1, 0, 1, 2\}, codomain \{3\}, rule \( f(x) = 3 \).

Would you like further details on this solution, or do you have any questions?

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Here are 5 related questions for practice:
1. What is the definition of a one-to-one function?
2. How can you determine the range of a function from a diagram?
3. Can a function have the same output for different inputs? Explain with examples.
4. What is the difference between codomain and range in a function?
5. How can we represent a function rule mathematically from a set of mappings?

**Tip**: Always verify if each input in a set is associated with only one output to determine if a relation is a function.

Dari himpunan A dan B berikut, manakah yang merupakan fungsi? Sebutkan pula domain, kodomain, dan rumusnya.

Analyze the sets A and B to determine which diagrams represent a function. Identify the domain, codomain, and formula for each valid function. This problem covers the basics of set theory and functions, suitable for Grades 10-12.

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