I Give Up! What is the Right Answer and How Do I Figure It Out?!

Question

Round the answers to two decimal places as needed.

A local carpet cleaning company charges $11.28 for each room plus a reservation fee of $8. They clean a maximum of 11 rooms. Also, they have the policy that once a reservation is made, if you cancel, the reservation fee is non-refundable. Let C represent the total cost from the carpet cleaning company and x represent the number of rooms cleaned

What is the practical domain of this function?

Practical Domain: ___________ ≤ x ≤ ___________

What is the practical range of this function?

Practical Range: __________ ≤ C (x) ≤ __________

Answer 1

In this question, x is the number of rooms cleaned. The practical domain is the range in possible rooms cleaned. The smallest number of rooms to be cleaned is 0 and we are told the maximum number of rooms they can clean is 11.

So Practical Domain: 0 rooms ≤ x ≤ 11 rooms.

C(x) is the cost to the cleaning company. Each room costs $11.28 to clean. Also if any rooms are cleaned they charge a reservation fee of $8.

So, C(x) = $11.28x + $8; if x > 0.

If x = 0, then there is no reservation fee, so C(0) = $0.

Practical range is the smallest and largest possible values of C(x) considering the practical domain.

The smallest C(x) would be if x = 0, then C(x) = $0.

The largest C(x) would be if x = 11, then C(x) = $11.28 * 11 + $8 = $124 + $8 = $132

Practical Range:  $0 ≤ C (x) ≤  $132