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To solve the problem, we need to identify both the domain and range of the function that models the situation.

### Problem Summary:
- The venue can be rented for either **1, 2, or 3 hours**.
- The cost per hour is **$275**.

### Domain:
- The domain represents the possible **number of hours** the venue can be rented. Since the venue can be rented for 1, 2, or 3 hours, the domain is the set $\{1, 2, 3\}$.

### Range:
- The range represents the possible **total cost** based on the rental time. The total cost is given by:
  \[
  \text{Cost} = 275 \times \text{Number of hours}.
  \]
  For:
  - 1 hour, the cost is $275 \times 1 = 275$,
  - 2 hours, the cost is $275 \times 2 = 550$,
  - 3 hours, the cost is $275 \times 3 = 825$.
  
  Therefore, the range is $\{275, 550, 825\}$.

### Correct Answer:
- **Domain**: $\{1, 2, 3\}$
- **Range**: $\{275, 550, 825\}$

Thus, the correct answer is **Option D**.

Let me know if you would like more details or have any further questions.

Here are 5 related questions to expand your understanding:
1. How would the domain change if the venue could be rented for any number of hours between 1 and 3?
2. What would be the range if the cost per hour was increased to $300?
3. How do you determine the range of a function if the hourly rate changes based on the number of hours rented?
4. What type of function models this situation? Is it linear or another type?
5. How would the domain and range change if fractional hours were allowed?

**Tip**: When determining the domain of a real-world function, always consider what values make sense for the given context (e.g., time and cost can't be negative).

A venue for a dance recital can be rented for $275 per hour. The venue can be rented for either 1 hour, 2 hours, or 3 hours. The cost in dollars to rent the pool is a function of the number of hours the venue is rented. What are the domain and range of the function for this situation?

Explore how to determine the domain and range of a function modeling the cost to rent a venue at $275 per hour for 1, 2, or 3 hours. This problem involves basic linear functions and is suitable for Grades 8-10.

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