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The diagram shows a relation between two sets, where the left set contains the elements {13, 17, 5}, and the right set contains {11, 14}. We need to determine whether this relation defines a function and also provide the domain and range.

### 1. **Is this relation a function?**
To qualify as a function, each element of the domain (the set on the left) must map to exactly one element in the range (the set on the right). Upon reviewing the arrows:

- 13 maps to 11.
- 17 maps to 11.
- 5 maps to 14.

Each element of the domain maps to exactly one element in the range. Therefore, this **is a function**.

### 2. **Domain and Range**
- The **domain** is the set of all inputs (the elements from the first set): \{13, 17, 5\}.
- The **range** is the set of all outputs (the elements from the second set that are mapped by at least one input): \{11, 14\}.

### Answer Explanation:
- **The relation defines a function** since each element of the domain maps to one element in the range.
- The **domain** is \{13, 17, 5\}.
- The **range** is \{11, 14\}.

### Correct multiple-choice answers:
- The correct answer to whether this is a function is **A**: "Yes, because each element of the domain (first component) is distinct and corresponds to exactly one range element (second component)."
- For the domain, you should select the answer where the domain is the set **\{13, 17, 5\}**.

Do you want further explanation on any part?

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### 5 Follow-Up Questions:
1. What makes a relation not a function?
2. How is the range determined in a function?
3. Can a function map multiple domain elements to the same range element?
4. How do you find the domain and range in more complex functions, like those involving variables?
5. What are some examples of relations that are not functions?

### Tip:
Always check if any domain element maps to more than one range element when determining whether a relation is a function!

Determine whether the relation defines a function, and give the domain and range.

Learn how to determine if a given relation is a function by analyzing whether each domain element maps to exactly one range element. Understand how to find the domain and range of a relation. Suitable for middle school math students.

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