https://r2.erweima.ai/mathbot/image/1726967241886byta4p6x.jpg

The diagram you've provided represents a relation between two sets. One set contains the numbers \( 2 \) and \( 4 \), and the other set contains the letters \( a \), \( b \), \( c \), and \( d \). The arrows indicate how elements from the first set (on the left) are related to elements in the second set (on the right).

To determine if this is a **function**, we need to check whether every element in the first set is related to exactly one element in the second set. Specifically:

- An element from the first set (domain) can only map to one element in the second set (codomain) in a function.

### Analysis of the diagram:
- The number \( 2 \) maps to both \( a \) and \( b \), meaning it has two outputs.
- The number \( 4 \) maps to \( b \), \( c \), and \( d \), so it has three outputs.

Because elements from the first set (like \( 2 \) and \( 4 \)) map to multiple elements in the second set, **this is not a function**. Instead, it is a **relation**.

A **function** requires that each input (element from the left set) is paired with exactly one output (element from the right set), and that condition is not met here.

Would you like further details on how relations differ from functions or how to identify functions from similar diagrams?

### Related Questions:
1. How can you tell when a relation is a function?
2. What are some examples of common types of functions?
3. Can a function have the same output for two different inputs?
4. How does the vertical line test work for functions on graphs?
5. What is the difference between injective, surjective, and bijective functions?

**Tip:** In a function, no element from the domain can have more than one arrow pointing to different elements in the codomain.

Learn how to analyze a diagram to determine if it represents a function or a relation. This tutorial explains the conditions required for a function, including the unique mapping from each element in the domain to the codomain. Suitable for students in Grades 6-8.

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