To find the domain and range of the given relation, we need to identify all the unique $x$-values and $y$-values in the set of ordered pairs.

Given relation: $\{(0, 3), (-9, 2), (-1, -3), (-3, -1)\}$

Domain

The domain is the set of all possible $x$-values in the relation.

• From the pairs, the $x$-values are: $0$, $-9$, $-1$, and $-3$.
• Therefore, the domain is: $\{0, -9, -1, -3\}$.

Range

The range is the set of all possible $y$-values in the relation.

• From the pairs, the $y$-values are: $3$, $2$, $-3$, and $-1$.
• Therefore, the range is: $\{3, 2, -3, -1\}$.

Summary

• Domain: $\{0, -9, -1, -3\}$
• Range: $\{3, 2, -3, -1\}$

Would you like more details on this solution or have any questions?

---

Here are some related questions:

1. How do you determine the domain and range for a function versus a relation?
2. What are some common types of relations in mathematics?
3. How can we visually represent the domain and range of a relation?
4. What is the difference between a finite and infinite domain?
5. How does the concept of domain and range apply to real-world situations?

Tip: For any relation, the domain includes all distinct $x$-values, while the range includes all distinct $y$-values.