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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?

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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.

What are the domain and range of this relation? (-10, -3), (-10, 9), (2, 9), (10, 10), (-5, 0)

Learn how to find the domain and range of a given relation with ordered pairs (-10, -3), (-10, 9), (2, 9), (10, 10), and (-5, 0). This solution provides a step-by-step approach to identifying unique x- and y-values.

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