{(2, 6), (3, 8), (3, -2), (4, 7), (3, 1)}

Select the correct DOMAIN.

Select the correct RANGE.

Decide whether this is a function.

*You should select 3 answers from the options below*

To solve this problem, let's break it down step by step:

### 1. **Domain**  
The domain refers to the set of all **input values** or **x-values** of the given points. Looking at the set of points:  
\[
(2, 6), (3, 8), (3, -2), (4, 7), (3, 1)
\]
The **x-values** (input values) are:  
\[
\{2, 3, 3, 4, 3\}
\]
The unique values in the domain are:  
\[
\{2, 3, 4\}
\]

### 2. **Range**  
The range refers to the set of all **output values** or **y-values**. Looking at the points:  
\[
(2, 6), (3, 8), (3, -2), (4, 7), (3, 1)
\]
The **y-values** (output values) are:  
\[
\{6, 8, -2, 7, 1\}
\]
Thus, the range is:  
\[
\{6, 8, -2, 7, 1\}
\]

### 3. **Is this a function?**  
A relation is a function if every input (x-value) has **exactly one output** (y-value).  
Looking at the x-values, we see that \(x = 3\) appears multiple times with different y-values:  
\[
(3, 8), (3, -2), (3, 1)
\]
Since the input \(x = 3\) corresponds to multiple outputs (8, -2, 1), this is **not a function**.

### Correct Answers:
- **Domain:** \(\{2, 3, 4\}\)
- **Range:** \(\{6, 8, -2, 7, 1\}\)
- **Is this a function?** No, it is not a function.

Would you like more details on this explanation?  

Here are some related questions:
1. What is the definition of a domain in a mathematical function?
2. How does the range differ from the domain?
3. What is the vertical line test for determining a function?
4. How do you find the domain and range from a graph?
5. What are examples of relations that are not functions?

**Tip:** Always check if every input has exactly one output when deciding if a relation is a function.

Select the correct DOMAIN, RANGE, and decide if the set of points {(2, 6), (3, 8), (3, -2), (4, 7), (3, 1)} is a function.

Determine the domain, range, and whether the relation {(2, 6), (3, 8), (3, -2), (4, 7), (3, 1)} is a function. Learn how to identify key properties of functions based on input-output pairs. Suitable for students in Grades 8-10.

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