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The image contains a question asking to analyze a function \( f(A) \), where sets \( A = \{1, 2, 4\} \), \( B = \{1, 2, 4, 5\} \), and a range \( A \to B \) are given, and the task is to determine the graph of the function \( f \) that defines it as a relation between these sets.

To assist you properly, I will solve the question step by step based on the information in the image:

1. The function must assign each element in \( A \) to an element in \( B \).
2. Analyze each choice to see which graph satisfies these conditions as a proper function mapping.

Now, let's look at the given function options:

- Option A: Graph is \( \{(1, 1), (2, 1), (4, 2)\} \)
- Option B: Graph is \( \{(1, 2), (2, 1), (4, 2), (1, 1)\} \)
- Option C: Graph is \( \{(1, 5), (2, 1), (4, 4)\} \)
- Option D: Graph is \( \{(1, 2), (2, 4), (1, 4), (4, 2)\} \)

### Explanation:
A function requires that each element in set \( A \) maps to exactly one element in set \( B \).

- **Option A** correctly maps each element of \( A \) to one element in \( B \). Therefore, this is a valid function.
- **Option B** repeats the element \( 1 \) twice, mapping it to both \( 1 \) and \( 2 \), which violates the definition of a function.
- **Option C** is a valid function, as each element in \( A \) is uniquely mapped to an element in \( B \).
- **Option D** violates the rule of a function because it maps \( 1 \) to both \( 2 \) and \( 4 \).

### Conclusion:
Options A and C are valid functions. Therefore, the correct answer will be the one that aligns with the problem's specific instructions, which likely call for only one function.

Would you like further details or clarification on any of the steps? Here are some related questions to deepen your understanding:

1. What is the formal definition of a function in set theory?
2. Can a function map an element of set \( A \) to more than one element in set \( B \)?
3. What distinguishes a relation from a function?
4. How does the choice of range affect the definition of a function?
5. How do you determine if a graph represents a valid function?

**Tip:** Always remember that in a function, every element in the domain must map to exactly one element in the range.

Given the sets A={1,2,4} and B={1,2,4,5}, determine the graph of the function f: A -> B.

Analyze the function f: A={1,2,4} -> B={1,2,4,5} and determine the correct graph representation. This problem covers set theory concepts, including the definition of a function and its graph. Suitable for students in Grades 10-12.

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