The function f(x) = 2.5x models the amount of water, in quarts, in a bucket after x seconds. Sally needs to fill a 55-quart bucket. Which is the most appropriate domain for the function?

Domain: 0 ≤ x ≤ 22

Step-by-step explanation:

Given

f(x) = 2.5x

Required

Determine the domain of the function

From the question, we understand that the size of the bucket is 55 quarts

This means the maximum of the range is 55.

In other words, the maximum value of f(x) is 55

Substitute 55 for f(x) in f(x) = 2.5x

55 = 2.5x

2.5x = 55

Make x the subject

x = 55/2.5

x = 22

Also, we understand that x represents time and it's impossible to have a negative time.

So, the minimum value x can get is

x = 0

The domain can then be represented as:

Minimum ≤ x ≤ Maximum

This gives:

0 ≤ x ≤ 22

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