To determine the domain and range of the given relation, we need to analyze each ordered pair in the relation:

Relation:

• (-10, -3)
• (-10, 9)
• (2, 9)
• (10, 10)
• (-5, 0)

Step 1: Find the Domain

The domain consists of all the unique $x$-values in the ordered pairs:

• $x$-values: -10, -10, 2, 10, -5
• Unique $x$-values: $-10, -5, 2, 10$

Thus, the domain is $\{-10, -5, 2, 10\}$.

Step 2: Find the Range

The range consists of all the unique $y$-values in the ordered pairs:

• $y$-values: -3, 9, 9, 10, 0
• Unique $y$-values: $-3, 0, 9, 10$

Thus, the range is $\{-3, 0, 9, 10\}$.

Answer

The correct answer from the choices is:

• Domain: $\{-10, -5, 2, 10\}$
• Range: $\{-3, 0, 9, 10\}$

This matches the third option.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. How would the domain and range change if another point, such as $(0, 5)$, was added?
2. What is the difference between a relation and a function?
3. Can a relation have duplicate $x$-values and still be considered a function?
4. How can you graphically represent the domain and range of a relation?
5. What does it mean for a relation to have a finite domain and range?

Tip: In a relation, if an $x$-value appears more than once with different $y$-values, the relation is not a function.