Question

select the correct answer.
stanley is filling a water tank that already has 10 gallons of water in it. he is filling the tank at the rate of 4.75 gallons per minute. this situation is represented by the following function, where n is the number of minutes.
$f(n) = 10 + 4.75n$
if stanley fills the tank for a maximum of 10 minutes, which of the following represents the domain and range of the given function?

• d: $0 \leq n \leq 10$

r: $0 \leq f(n) \leq 57.5$

• d: $10 \leq f(n) \leq 57.5$

r: $0 \leq n \leq 10$

• d: $0 \leq f(n) \leq 57.5$

r: $0 \leq n \leq 10$

• d: $0 \leq n \leq 10$

r: $10 \leq f(n) \leq 57.5$

Explanation:

Step1: Determine the domain

The variable \( n \) represents the number of minutes Stanley fills the tank. He fills it for a maximum of 10 minutes, and the number of minutes can't be negative. So the domain (values of \( n \)) is \( 0 \leq n \leq 10 \).

Step2: Determine the range

The function is \( f(n)=10 + 4.75n \). When \( n = 0 \), \( f(0)=10+4.75(0)=10 \). When \( n = 10 \), \( f(10)=10 + 4.75(10)=10 + 47.5 = 57.5 \). Since the function is linear and increasing (the coefficient of \( n \) is positive), the range (values of \( f(n) \)) is \( 10 \leq f(n) \leq 57.5 \).

Answer:

D: \( 0 \leq n \leq 10 \)
R: \( 10 \leq f(n) \leq 57.5 \) (the last option among the given choices)