Question

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+4.75nIf 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 ≤ n ≤ 10R: 0 ≤ f(n) ≤ 57.5 D: 0 ≤ f(n) ≤ 57.5R: 0 ≤ n ≤ 10 D: 0 ≤ n ≤ 10R: 10 ≤ f(n) ≤ 57.5 D: 10 ≤ f(n) ≤ 57.5R: 0 ≤ n ≤ 10

Answer 1

Step 1

Find the domain of the function

`\begin{gathered} f(n)=10\text{ +4.75n} \\ \text{The domain refers to n} \\ \text{The max value for n = 10 minutes} \\ \text{The minimum value for n = 0 minutes} \end{gathered}`

Hence the domain is given as

`\begin{gathered} n\leq10 \\ \text{and} \\ n\ge0 \\ To\text{ gether, we will have} \\ \text{Domain (D) : 0}\leq n\leq10 \end{gathered}`

Step 2

Find the range of the function.

`\begin{gathered} f(n)\text{ = 10 + 4.75n} \\ \text{The maximum value for the rangef(n) is when n = 10} \\ f(10)\text{ = 10 + 4.75(10)=57.5} \\ \text{The minimum value for f(n) is when n =0} \\ f((0)\text{ = 10 + 4.75(0)= 10} \\ \end{gathered}`

Hence, the range (f(n)) is given as

`\begin{gathered} f(n)\ge10 \\ \text{and} \\ f(n)\leq57.5 \\ \text{Together, } \\ \text{Range(R) : 10}\leq f(n)\leq\text{ 57.5} \end{gathered}`