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?A.Domain: all real numbersRange: all real numbersB.Domain: all integers ≥ 0Range: all integers ≥ 0C.Domain: {275, 550, 825}Range: {1, 2, 3}D.Domain: {1, 2, 3}Range: {275, 550, 825}

In this situation, the cost to rent the venue is a function of the number of hours rented. Let's break down the domain and range.

- **Domain**: The number of hours the venue can be rented for, which is either 1, 2, or 3 hours.
- **Range**: The corresponding cost, which would be $275$ for 1 hour, $550$ for 2 hours, and $825$ for 3 hours.

### Let's evaluate the options:
- **Option A**: 
  - **Domain**: "All real numbers" doesn't make sense, since you can't rent the venue for fractional or negative hours.
  - **Range**: "All real numbers" doesn't apply either because the cost is limited to discrete values (275, 550, 825).
  - This is **incorrect**.

- **Option B**:
  - **Domain**: "All integers ≥ 0" would allow any non-negative integer, but you can only rent the venue for 1, 2, or 3 hours.
  - **Range**: "All integers ≥ 0" is incorrect for the same reason, as the cost is limited to specific values.
  - This is **incorrect**.

- **Option C**:
  - **Domain**: {275, 550, 825} refers to the cost, not the hours.
  - **Range**: {1, 2, 3} refers to the hours, not the cost.
  - The domain and range are swapped.
  - This is **incorrect**.

- **Option D**:
  - **Domain**: {1, 2, 3} represents the number of hours, which is correct.
  - **Range**: {275, 550, 825} represents the cost for renting the venue, which is correct.
  - This is **correct**.

### Answer:
**Option D: Domain: {1, 2, 3}, Range: {275, 550, 825}**

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the domain change if half-hour rentals were allowed?
2. How do you define a function's domain and range in general?
3. What would the total cost be if you rented the venue for 2 hours and 30 minutes?
4. How would the range change if the hourly rental rate increased by $50?
5. Could the domain be extended to include fractional hours? How?

**Tip:** Always check whether the function deals with discrete or continuous values when determining the domain and range.

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? A. Domain: all real numbers Range: all real numbers B. Domain: all integers ≥ 0 Range: all integers ≥ 0 C. Domain: {275, 550, 825} Range: {1, 2, 3} D. Domain: {1, 2, 3} Range: {275, 550, 825}

Find the domain and range of a function representing the cost to rent a venue for $275 per hour. This problem helps students understand how to determine domain and range for discrete values. Suitable for Grades 6-8 students, covering functions and their practical applications.

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