Let's consider the given information step-by-step:
1. Understanding the function:
We have the function [tex]\( L = 2D + 200 \)[/tex], which describes the length of the road [tex]\( L \)[/tex] as a function of the number of days [tex]\( D \)[/tex] the crew has worked. This tells us that for each value of [tex]\( D \)[/tex], we can determine a corresponding value of [tex]\( L \)[/tex].
2. Identifying the domain:
The domain of a function is the set of all possible input values (in this case, values of [tex]\( D \)[/tex]) that the function can take. According to the problem, the crew can work for at most 60 days. Therefore, the number of days [tex]\( D \)[/tex] can range from 0 to 60.
So, the correct description of the domain is "number of days the crew has worked" and the set of values is [tex]\( D ∈ [0, 60] \)[/tex].
3. Identifying the range:
The range of a function is the set of all possible output values (in this case, values of [tex]\( L \)[/tex]) that the function can produce. Given that [tex]\( D \)[/tex] ranges from 0 to 60, we can find the corresponding range for [tex]\( L \)[/tex]:
- When [tex]\( D = 0 \)[/tex]:
[tex]\( L = 2(0) + 200 = 200 \)[/tex]
- When [tex]\( D = 60 \)[/tex]:
[tex]\( L = 2(60) + 200 = 320 \)[/tex]
Thus, the length of the road [tex]\( L \)[/tex] will range from 200 miles to 320 miles.
So, the correct description of the range is "length of the road (in miles)" and the set of values is [tex]\( L ∈ [200, 320] \)[/tex].
4. Filling in the table correctly:
[tex]\[
\begin{tabular}{|l|l|l|}
\hline
& Description of Values & Set of Values \\
\hline Domain: & \begin{tabular}{l}
O length of the road (in miles) \\
✔ number of days the crew has worked \\
\end{tabular} & \( D ∈ [0, 60] \) \\
\hline Range: & \begin{tabular}{l}
✔ length of the road (in miles) \\
O number of days the crew has worked \\
\end{tabular} & \( L ∈ [200, 320] \) \\
\hline
\end{tabular}
\][/tex]
In conclusion:
- The domain represents the number of days the crew has worked and is [tex]\( D ∈ [0, 60] \)[/tex].
- The range represents the length of the road (in miles) and is [tex]\( L ∈ [200, 320] \)[/tex].
