Question

a construction crew is lengthening a road. let (l) be the total length of the road (in miles). let (d) be the number of days the crew has worked. suppose that (l = 4d+400) 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.

description of values	set of values
range: number of days the crew has worked<br>length of the road (in miles)	the set of all real numbers from 400 to 640<br>the set of all real numbers from 4 to 400<br>the set of all real numbers from 0 to 60<br>(4,8,12,16,cdots)<br>(60,61,62,63,cdots,640)<br>(0,1,2,3,cdots,400)

Explanation:

Step1: Determine the domain

The crew can work for at most 60 days. The domain is the set of all possible input values (independent variable). Here, the independent variable is the number of days $D$ the crew has worked. Since the number of days is a non - negative integer and at most 60, the domain is the set of all whole numbers from 0 to 60, i.e., $\{0,1,2,\cdots,60\}$.

Step2: Determine the range

We have the function $L = 4D+400$. When $D = 0$, $L=4\times0 + 400=400$. When $D = 60$, $L=4\times60+400=240 + 400=640$. Since $L$ is a linear function of $D$ and $D$ ranges from 0 to 60, the range is the set of all real numbers from 400 to 640.

Answer:

Domain: the set of all whole numbers from 0 to 60
Range: the set of all real numbers from 400 to 640