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

In this situation, the cost to rent the venue depends on the number of hours it is rented, and the function can only take on certain discrete values based on the given rental hours.

1. **Domain**: This represents the number of hours the venue is rented. The problem states that the venue can be rented for either 1 hour, 2 hours, or 3 hours. So, the domain is {1, 2, 3}.

2. **Range**: This represents the cost for renting the venue. The cost is calculated by multiplying the number of hours by $275. So, for:
   - 1 hour, the cost is $ 1 \times 275 = 275 $ dollars,
   - 2 hours, the cost is $ 2 \times 275 = 550 $ dollars,
   - 3 hours, the cost is $ 3 \times 275 = 825 $ dollars.

Thus, the range is {275, 550, 825}.

Therefore, the correct answer is:

**B. Domain: {1, 2, 3} Range: {275, 550, 825}**

Would you like a detailed explanation of the process, or do you have any further questions?

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**Related Questions:**
1. How would the domain and range change if the venue could be rented for up to 5 hours?
2. What is the cost for renting the venue for 4 hours, assuming it’s an option?
3. If the cost per hour increased to $300, what would the new range be for the original domain?
4. Can the domain ever include non-integer values, and why?
5. How would you represent this function graphically?

**Tip:** Always identify the independent (domain) and dependent (range) variables clearly to avoid confusion.

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 for a function representing the cost to rent a venue for a dance recital. Given a rate of $275 per hour, this problem helps students learn key mathematical concepts such as functions, domain, and range. Suitable for students in Grades 6-8.

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