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


Let's break down the problem.

The cost to rent the venue is \$275 per hour, and the venue can be rented for either 1, 2, or 3 hours. Therefore:

- For 1 hour, the cost is \$275.
- For 2 hours, the cost is \$275 × 2 = \$550.
- For 3 hours, the cost is \$275 × 3 = \$825.

This establishes a clear relationship between the number of hours rented and the cost:

- **Domain**: The domain represents the input values, which are the number of hours the venue can be rented. Since the venue can only be rented for 1, 2, or 3 hours, the domain is {1, 2, 3}.
- **Range**: The range represents the possible output values, which are the corresponding costs for renting the venue. These costs are \$275, \$550, and \$825, so the range is {275, 550, 825}.

### Correct Answer:
**B. Domain: {1, 2, 3}; Range: {275, 550, 825}**

Would you like more details or have any questions?

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Here are 5 related questions for deeper exploration:
1. How would the function change if the cost per hour increased to \$300?
2. What if the venue could be rented for a fractional number of hours, such as 1.5 or 2.5?
3. What type of function describes this situation—linear, quadratic, or something else?
4. How would the domain and range change if the venue could be rented for any number of hours from 1 to 5?
5. Can the relationship between hours and cost be represented using a graph? How would it look?

**Tip:** Always check whether a function's domain and range are discrete (specific values) or continuous, as this determines the nature of the problem.

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

Understand the domain and range of the function describing the cost to rent a venue for $275 per hour. This problem covers key mathematical concepts of functions, domain, and range, suitable for students in Grades 6-8.

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