Answer:
D: 0 ≤ n ≤ 10
R: 10 ≤ f(n) ≤ 57.5
Step-by-step explanation:
In the given situation, the amount of water in the tank, f(n), depends on the number of minutes, n.
So, n is the independent variable and f(n) is the dependent variable.
The domain of a function is the set of all input values for the independent variable, n.
Stanley fills the tank for a maximum of 10 minutes. The possible number of minutes can range from 0 minutes to 10 minutes.
So, the domain of the function is D: 0 ≤ n ≤ 10.
The range of a function is the set of all output values for the dependent variable, f(n).
Stanley is filling the tank at the rate of 4.75 gallons per minute. Before he begins filling the tank, when n = 0 minutes, the tank already holds 10 gallons of water.
If Stanley fills the tank for 10 minutes, the amount of water in the tank will be 10 gallons, plus the 4.75 gallons of water filled during each of the 10 minutes.
f ( n ) = 10 + 4.75n
f ( 10 ) = 10 + 4.75 ( 10 )
= 10 + 4.75
= 57.5
The amount of water in the tank can range from 10 gallons to 57.5 gallons.
So, the range of the function is R: 10 ≤ f(n) ≤ 57.5.
