https://file.aiquickdraw.com/mathbot/file/17272246339506nf42e42.jpg

Let's analyze the problem in the image.

### Problem:
The problem asks to:
1. Identify the correct domain and range for a given relation.
2. Determine whether the relation represents a function.

### First, the domain and range:
The provided diagram illustrates a relation between two sets:
- **Set 1 (Domain)**: It contains plant types such as "Shrub", "Daisy", and "Herb".
- **Set 2 (Range)**: It contains names of plants such as "Basil", "Rose", "Oak", and "Flower".

### Mapping:
The arrows in the diagram indicate the relationship between elements of the domain and range:
- **Shrub** maps to **Basil**.
- **Shrub** also maps to **Rose**.
- **Daisy** maps to **Flower**.
- **Herb** maps to **Oak**.
- **Tree** maps to **Oak**.

### Analyzing the domain and range:
- **Domain**: The elements that are being mapped from: Shrub, Daisy, Herb, Tree.
- **Range**: The elements that are being mapped to: Basil, Rose, Flower, Oak.

So, the correct domain is: \(\{\text{Shrub}, \text{Daisy}, \text{Herb}, \text{Tree}\}\).  
The correct range is: \(\{\text{Basil}, \text{Rose}, \text{Flower}, \text{Oak}\}\).

### Determining whether this is a function:
A relation is a function if every element in the domain is mapped to exactly **one** element in the range.
- **Shrub** is mapped to both **Basil** and **Rose**, which means one element in the domain is mapped to more than one element in the range.

Thus, this relation is **not** a function.

### Conclusion:
The correct answer would be:
- Domain: \(\{\text{Shrub}, \text{Daisy}, \text{Herb}, \text{Tree}\}\)
- Range: \(\{\text{Basil}, \text{Rose}, \text{Flower}, \text{Oak}\}\)
- The relation **does not represent a function** because an element in the first set (Shrub) corresponds to more than one element in the second set.

This corresponds to the following options in the image:
- **Domain**: Shrub, Daisy, Herb, Tree.
- **Range**: Basil, Rose, Flower, Oak.
- **Option B**: "No, because each element in the first set corresponds to exactly one element in the second set."

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Would you like more details on how relations and functions work?

Here are 5 related questions to expand on this:
1. What are the differences between a relation and a function?
2. How can you determine if a relation is a function from its graph?
3. What are examples of real-world functions?
4. Can a function have multiple outputs for a single input?
5. How do you represent functions using set notation?

**Tip**: A function assigns **exactly one** output to each input. If any input has more than one output, the relation is not a function.

State the domain and range for the following relation. Then determine whether the relation represents a function.

Learn how to determine the domain and range of a relation and assess whether it is a function. This problem includes set theory concepts and function analysis, where multiple elements in the domain map to the range. Suitable for Grades 7-9.

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