https://file.aiquickdraw.com/mathbot/file/1727225741234tc0crw15.jpg

The image shows a function \( g: A \to B \) defined by an arrow diagram. The function maps elements from set \( A \) to set \( B \), where:

- Set \( A = \{1, 2, 3, 4\} \)
- Set \( B = \{1, 2, 3\} \)

The mappings are as follows:
- \( g(1) = 1 \)
- \( g(2) = 2 \)
- \( g(3) = 3 \)
- \( g(4) = 3 \)

We are asked to classify this function according to the provided options:

1. **A. Constant function**: A constant function assigns the same value to every element in the domain, which is not the case here, as each element in \( A \) is not mapped to the same value in \( B \).

2. **B. Surjective (onto) function**: A surjective function is one where every element in the codomain \( B \) has at least one preimage in \( A \). Here, every element in \( B \) (1, 2, 3) is the image of some element in \( A \), so this function is surjective.

3. **C. Bijective function**: A bijective function is both injective and surjective. Since this function is surjective but not injective (because both 3 and 4 map to 3, violating injectivity), it is not bijective.

4. **D. Injective (one-to-one) function**: A function is injective if every element in the domain maps to a unique element in the codomain. Here, \( g(3) = g(4) = 3 \), so it is not injective.

5. **E. Linear function**: A linear function typically applies to real numbers and is of the form \( g(x) = ax + b \). This function involves finite sets, so it doesn't apply here.

### Conclusion:
The function is **surjective (B)**.

Do you need further clarification, or have any questions? 

Here are 5 related questions for further exploration:

1. What is the difference between an injective and a surjective function?
2. How do you determine if a function is bijective from its arrow diagram?
3. Can a function be both injective and surjective, and what does that mean?
4. How would this function change if an element from set \( B \) was not mapped to any element from \( A \)?
5. What real-world examples can represent surjective functions?

**Tip**: When analyzing functions from a diagram, check carefully if every element in the domain and codomain is accounted for to classify the function correctly.

Ditentukan fungsi g: A → B yang didefinisikan sebagai diagram panah berikut.

Analyze a function defined by an arrow diagram mapping set A to set B, with a focus on surjective, injective, and bijective classifications. Learn how this function is classified as surjective.

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