https://file.aiquickdraw.com/mathbot/file/1727213905579zc18bqxs.jpg

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

### Definitions:
- **Function**: A relation where each element in the domain is associated with exactly one element in the range. In other words, no domain element is repeated with a different range value.

### Relation 1:
- Domain: {c, r, t, v}
- Range: {n, t, j, b}
- Each element in the domain has a unique corresponding value in the range. There are no repeated domain elements with different range values.
  - **Conclusion**: This is a function.

### Relation 2:
- Domain: {-1, -9, 9, 2, -2}
- Range: {desk, pencil, desk, sun, sun}
- Each element in the domain corresponds to a unique value in the range. Even though some range values are repeated (e.g., "desk" and "sun"), the domain elements are not.
  - **Conclusion**: This is a function.

### Relation 3:
- Set: \(\{(7, 3), (3, 6), (7, 2), (3, 7)\}\)
- Here, we see that the domain element "7" is associated with two different range values (3 and 2), and the domain element "3" is associated with two different range values (6 and 7).
  - **Conclusion**: This is **not** a function.

### Relation 4:
- Set: \(\{(z, -2), (a, -2), (z, -7), (e, 3)\}\)
- The domain element "z" is associated with two different range values (-2 and -7), which violates the rule for a function.
  - **Conclusion**: This is **not** a function.

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

Would you like a more detailed explanation or have any questions? 

Here are some related questions:
1. What is the difference between a function and a relation?
2. Can a function have the same range value for different domain values?
3. How would you represent a function using a graph?
4. What is the vertical line test, and how does it determine if a relation is a function?
5. Can a function have more than one output for a single input?

**Tip**: Remember that in a function, each input (domain element) must map to exactly one output (range element).

For each relation, decide whether or not it is a function. Relations include a table of domain and range values or sets of ordered pairs.

Learn how to determine if a relation is a function by analyzing the domain and range values. This problem covers relations, functions, and the concept of one-to-one mapping, making it suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation