https://file.aiquickdraw.com/mathbot/file/1729557532543v1v5junx.jpg

Let's analyze each relation to determine if it's a function.

### Relation 1:
- A function must assign each element in the domain to exactly one element in the range.
- In this case, the domain has "lake," "paper," "leaf," and "tree," each mapped to only one unique value in the range.
  - "lake" → 4
  - "paper" → 4
  - "leaf" → -6
  - "tree" → -6
- No domain element is paired with more than one range element, so **Relation 1 is a function**.

### Relation 2:
- In this relation, some elements of the domain have more than one output:
  - 4 → 8 and 4 → -1
  - 9 → -1 and 9 → 6
- Since a function cannot assign more than one output to the same input, **Relation 2 is not a function**.

### Relation 3:
- This is written as a set of ordered pairs: \((b, x), (b, t), (b, b), (b, n)\).
- The domain element "b" is paired with multiple different range elements (x, t, b, n), which violates the rule that each input must have exactly one output.
- Therefore, **Relation 3 is not a function**.

### Relation 4:
- The pairs are \((-5, e), (-7, k), (1, r), (-9, v)\).
- Each input is mapped to exactly one output, with no repetitions in the domain.
- Therefore, **Relation 4 is a function**.

### Summary:
1. **Relation 1**: Function
2. **Relation 2**: Not a function
3. **Relation 3**: Not a function
4. **Relation 4**: Function

Would you like more details or have any questions? 

Here are 5 related questions to consider:
1. What conditions must a relation satisfy to be classified as a function?
2. Can a function have multiple elements in the range mapped to the same domain element?
3. How can we visually identify functions using a mapping diagram?
4. What is the difference between injective and surjective functions?
5. How can we determine if a relation is a function from its graph?

**Tip:** To check if a relation is a function, remember the vertical line test for graphs or check if any input is paired with more than one output.

Identify whether each relation is a function or not based on the given mappings.

Determine whether each of the given relations qualifies as a function by analyzing their domain and range mappings. Learn how to identify functions and understand key concepts related to functions and relations. Suitable for students in Grades 8-10.

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