Question

A construction crew is lengthening a road. Let I be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that L = 3D + 200 gives L as a function of D. The crew can work for at most 60 days.Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.Onumber of days the crew has worked Olength of the road (in miles)?Onumber of days the crew has worked Olength of the road (in miles)?

Answer 1

Step-by-step explanation

The domain of a function is the set of all values for which the function is defined. In this case, we can see that the function depends of the variable D, which represents the number of days the crew has worked.

Since the crew can work for at most 60 days and the time can not be negative, the domain of the function is the set of all real numbers from 0 to 60.

On the other hand, the range of a function is the set of all values that the function takes. In this case, we can see that the dependent variable is L, which represents the length of the road. Then, we have:

`\begin{gathered} L=3D+200 \\ \text{ If }D=0 \\ L=3(0)+200 \\ L=0+200 \\ L=200 \\ \\ \text{ If }D=60 \\ L=3\left(60\right)+200 \\ L=180+200 \\ L=380 \end{gathered}`

Thus, the range of the given function is the set of all real numbers from 200 to 380.

Answer