Question

Find the DOMAIN and RANGE for the following:

Mary is filling a pool over a 15-hour period. The pool started with 2,500 gallons and has a capacity of 15,000 gallons. The function g(h) = 850h + 2000 gives the number of gallons in the pool. What is the reasonable domain and range for this statement?
A. Domain: [0, 15]; Range: [2500, 15000]
B. Domain: [0, 15000]; Range: [2500, 15000]
C. Domain: [0, 15]; Range: [0, 15000]
D. Domain: [0, 15000]; Range: [0, 15000]

Answer 1

The domain for the function representing the number of gallons in the pool as it fills over time is [0, 15], and the range is [2500, 15000]. The correct answer is A. Domain: [0, 15]; Range: [2500, 15000].

Step-by-step explanation:

The reasonable domain for the function g(h) = 850h + 2000, which gives the number of gallons in the pool, refers to the period over which Mary is filling the pool. Here, h represents the number of hours. Since the pool is being filled over a 15-hour period, the domain is the interval from 0 to 15 hours, which can be denoted as [0, 15].

The range of this function represents the volume of water in the pool measured in gallons. It starts with 2,500 gallons and increases as the pool is filled, with the maximum capacity being 15,000 gallons. Therefore, the range is from the starting volume of 2,500 gallons to the maximum capacity of 15,000 gallons, expressed as [2500, 15000].

Given these considerations, the correct answer is:

• Domain: [0, 15]
• Range: [2500, 15000]

So, the answer is A. Domain: [0, 15]; Range: [2500, 15000].