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.