Respuesta :
We have been given the following function:
[tex]L=4D+200[/tex]where L represents the length of the road and D represents the number of days the crew has worked
In order to answer this question, we must first understand what domain and range are. Domain, in mathematical terms, represents the values that "x" can be (x is the independent variable on the horizontal axis of a graph). In this case, "x" is D, because the number of days directly affects the length of the road. The range represents the values "y" can be. In this case, "y" is L, because the length of the road changes in response to the number of days worked.
Let's start by figuring out the domain. We are given that the crew can work for at most 60 days. This means that the maximum value of D, or the DOMAIN, is 60. We also can assume that you cannot have negative days. Days start at 0 and go up to 60. In other words, the minimum value of the domain is 0. Therefore, Domain, which represents the number of days the crew has worked, is 0 ≤ x ≤ 60
Now, let's move on to the range, which represents the length of the road. The range is dependent on the domain. In this case, the minimum value of the domain causes a minimum range, and similarly, the maximum domain value causes a maximum range. The minimum occurs when D = 0, as we saw above. Let's figure out what L is when D = 0:
[tex]\begin{gathered} L=4(0)+200 \\ L=200 \end{gathered}[/tex]Now, let's figure out what L is when D = 60 (max domain value):
[tex]\begin{gathered} L=4(60)+200 \\ L=240+200 \\ L=440 \end{gathered}[/tex]Therefore, the Range, which represents the length of the road in miles, is 200 ≤ L ≤ 440
