https://file.aiquickdraw.com/mathbot/file/1725603970765d3lhahcf.jpg

The image shows four different relations and asks to identify which ones are functions. Based on the diagrams and the format, I can provide a detailed breakdown of each relation:

1. **Relation 1**:
   - It maps elements from the domain (left side) to the range (right side) using arrows.
   - Each element in the domain is mapped to only one element in the range.
   - This relation qualifies as a **function** because each input has exactly one output.

2. **Relation 2**:
   - Multiple elements from the domain map to elements in the range.
   - However, one domain element (likely “c”) is mapped to more than one element in the range.
   - This relation is **not a function** because one input (from the domain) has multiple outputs.

3. **Relation 3** (bottom-left):
   - There is a table showing the domain and range.
   - It looks like each domain element has exactly one corresponding range element.
   - This is a **function**, as no domain element is repeated in terms of mapping.

4. **Relation 4** (bottom-right):
   - This relation also displays a table for domain and range.
   - If a domain element repeats or maps to multiple range elements, it is not a function.
   - Judging from the visual, it seems to be a **function**, assuming no repeated mappings.

In summary:
- **Functions**: Relation 1, Relation 3, and Relation 4 (assuming no duplicate mappings in the table).
- **Not a function**: Relation 2.

Would you like a deeper explanation or additional details? Here are 5 follow-up questions to enhance your understanding:

1. What are the key characteristics of a function in set theory?
2. Can a function have the same range element for different domain elements?
3. How would you represent these relations using ordered pairs?
4. What makes a vertical line test helpful in determining whether a relation is a function?
5. How do domain and range tables help identify functions easily?

**Tip:** When checking if a relation is a function, remember the rule: every input (domain) must have only one output (range).

The image shows four different relations and asks to identify which ones are functions.

Learn how to identify functions by analyzing relation diagrams. Explore key concepts in set theory and relations, with visual examples of functions and non-functions. Suitable for students in Grades 8-10.

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