Question

Quiet You Family Daycare charges a rate of $75.00 a day plus $5.00 per diaper they have to change. Write an equation, in function notation, to represent this situation and state a reasonable domain and range.

A. C(d) = 75 + 5d; Domain: {d ≥ 0}, Range: {C ≥ 75}
B. C(d) = 5d - 75; Domain: {d ≥ 0}, Range: {C ≥ 0}
C. C(d) = 75d + 5; Domain: {d ≥ 0}, Range: {C ≥ 0}
D. C(d) = 75 + 5d; Domain: {d ≥ 0}, Range: {C ≥ 0}

Answer 1

The valid equation for the cost calculation at Quiet You Family Daycare is C(d) = 75 + 5d, with a domain of {d ≥ 0} and a range of {C ≥ 75}. The correct option is A.

Step-by-step explanation:

The correct equation to represent the cost C at Quiet You Family Daycare in function notation based on the number of diapers d changed is C(d) = 75 + 5d. This linear equation signifies that you pay a base rate of $75 per day, and for every diaper changed, there is an additional charge of $5. Considering the context, the domain and range represent all possible numbers of diapers and costs. The domain is the set of all non-negative integers for diapers since you can't change a negative number of diapers. Hence, the domain is {d ≥ 0}, which translates to 'd is greater than or equal to 0'. The range starts at $75 (when no diapers are changed), and it increases by $5 for each additional diaper, so the range is {C ≥ 75} which indicates 'C is greater than or equal to 75'. Therefore, the correct choice is A. By comparison, option B is incorrect because it suggests the cost could be less than the base rate, which isn't possible. Option C incorrectly multiplies the daily rate by the number of diapers, and option D has an incorrect range because the cost cannot be less than the daily base rate of $75.