Let's analyze the graph in the image you provided.

1. Domain: The domain of a relation is the set of all possible input values (x-values). Looking at the graph, the x-values correspond to the horizontal axis. The points plotted in the graph have the following x-values: $-1$, $0$, and $1$. Therefore, the domain is: $\text{Domain} = \{-1, 0, 1\}$

2. Range: The range of a relation is the set of all possible output values (y-values). The y-values correspond to the vertical axis. The points on the graph have the following y-values: $-1$, $0$, and $1$. Therefore, the range is: $\text{Range} = \{-1, 0, 1\}$

3. Function check: To determine if the relation is a function, we apply the vertical line test. If a vertical line passes through more than one point on the graph, then the relation is not a function. In this case, each vertical line drawn through any x-value ($-1$, $0$, or $1$) intersects the graph at exactly one point. Therefore, this relation is a function.

Summary:

• Domain: $\{-1, 0, 1\}$
• Range: $\{-1, 0, 1\}$
• Is it a function?: Yes

Would you like further details on any part of this explanation?

Here are some related questions for deeper understanding:

1. How can you check if a relation is a function using ordered pairs?
2. What does the vertical line test mean in terms of real-life examples of functions?
3. How do we find the domain of a relation when no graph is provided?
4. What are some examples of relations that are not functions?
5. How would the domain and range change if the graph were extended?

Tip: Always remember, a function cannot assign multiple outputs to the same input!