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.