https://file.aiquickdraw.com/mathbot/file/1729573167579uymh0441.jpg

One relation is a function and one is not. Identify each and explain.

In the image, there are two sets of relations depicted using arrow diagrams. Let’s analyze them individually to determine which is a function and which is not.

### Left Diagram:
- The left side has the following mappings:
  - \( 5 \to 6 \)
  - \( 5 \to 1 \)
  - \( 7 \to 9 \)

**Explanation**:
- A **function** requires that each input (element from the first set) is mapped to exactly **one output**.
- Here, the element \( 5 \) is mapped to both \( 6 \) and \( 1 \), which violates the definition of a function.
  
Thus, the **left relation is not a function** because one input (5) is mapped to more than one output.

---

### Right Diagram:
- The right side has the following mappings:
  - \( 1 \to 7 \)
  - \( 6 \to 7 \)
  - \( 3 \to 7 \)

**Explanation**:
- Each input (1, 6, and 3) has exactly one output (7). 
- There are no inputs mapped to more than one output, satisfying the definition of a function.

Thus, the **right relation is a function** because each input is mapped to exactly one output.

---

Would you like more details on functions and relations, or any specific part of this explanation clarified?

Here are 5 related questions to explore further:
1. What is the difference between a one-to-one function and a many-to-one function?
2. Can a function have multiple inputs mapping to the same output?
3. How can we represent functions algebraically as opposed to using diagrams?
4. What are some real-world examples of relations that are not functions?
5. How does the vertical line test help determine if a relation is a function?

**Tip**: To check if a relation is a function, remember that no input should map to more than one output!

Learn how to determine if a relation is a function or not using arrow diagrams. This problem explores the concept of functions, where each input must map to exactly one output, and how violations of this rule make a relation not a function. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation