U3.L2.HW: Domain and Range: Question 30

Question

Round the answers to two decimal places as needed.

A local catering company charges $9.32 for each person plus a reservation fee of $12. They serve a maximum of 10 people. 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 catering company and x represent the number of people served.

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

The domain is the set of allowable x-values for the function C(x). X represents the number of people. The problem tells you the maximum number people. For the minimum, what's the smallest number of people you can have? Can you have negative people?

For the range, plug in the x-values from your minimum to your maximum value of x to get the minimum and maximum cost (C(x)). That's your range except if you cancel, you owe at least the $12 fee.

Answer 2

C(x) = 9.32x + 12

with limit of x=10

domain is 0< x < 10

range is 0 < C < 93.2+12 = $105.20 = maximum cost

in interval notation

domain: [0,10]

range: [0, 105.2]