Question

Asia tutors elementary students in math for $8.50 an hour. She charges by the hour, always rounding up to the nearest hour, and can only dedicate a maximum of 12 hours per week tutoring. Suppose the function P(x) gives the total amount paid per week after working x amount of hours. Describe an appropriate domain of this function.

a)x∈{0,1,2,3,...,12}
b)∈{0,1,2,3,...,12}∩x∈{0,1,2,3,...,12}∩Z (where Z represents the set of integers)
c)∈{0,1,2,3,...,12}∩x∈{0,1,2,3,...,12}∩N (where N represents the set of natural numbers)
d)∈{0,1,2,3,...,12}∩0x∈{0,1,2,3,...,12}∩N0 (where 0N0 represents the set of non-negative integers)

Answer 1

The correct domain for the function representing Asia's total pay after working x hours, rounding up to the nearest hour and with a 12-hour weekly limit, is {0,1,2,3,...,12}, which is option a).

Step-by-step explanation:

Asia tutors elementary students in math and charges by the hour, rounding up to the nearest hour, with a maximum of 12 hours per week dedicated to tutoring. The function P(x) gives the total amount paid per week after working x hours. The domain of this function should be the set of all possible hours Asia can work in a week, which includes only whole numbers since she cannot work a fraction of an hour and rounds up to the nearest hour. Therefore, the appropriate domain is {0,1,2,3,...,12} which represents the whole numbers from 0 to 12. The best choice is option a) because option b) is unnecessarily complex, option c) is incorrect as it refers to natural numbers which doesn't include zero, and option d) contains a strange notation that is irrelevant for this context.