The image shows a diagram with two sets and arrows between elements, which visually represents a relation. We want to determine if this relation is a function.

Key Concept: What is a Function?

A relation is considered a function if every element in the domain (input set) maps to exactly one element in the codomain (output set). In other words, each input should have a single unique output.

Analyzing the Diagram:

1. The domain contains four elements: $x_1, x_2, x_3, x_4$.
2. The codomain contains three elements: $1, 2, 3$.
3. The arrows indicate how each element of the domain maps to an element in the codomain:
   • $x_1$ maps to $1$.
   • $x_2$ maps to $2$.
   • $x_3$ maps to $2$.
   • $x_4$ maps to $3$.

Conclusion:

• Each element in the domain $\{ x_1, x_2, x_3, x_4 \}$ has exactly one arrow pointing to an element in the codomain.
• There is no input (element from the domain) that maps to more than one output.

Since each input has a unique output, this is a function.

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Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What is the difference between a function and a relation?
2. How can you tell if a function is one-to-one (injective)?
3. Can a function have the same output for different inputs?
4. How do you represent functions algebraically?
5. What is the vertical line test for functions?

Tip: Always check if each input has a unique output when determining if a relation is a function.