Questions: 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=2 D+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. - Description of Values Set of Values - Domain: - length of the road (in miles) - number of days the crew has worked - (Choose one) - Range: - length of the road (in miles) - number of days the crew has worked - (Choose one)

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=2 D+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.

- Description of Values Set of Values
- Domain:
- length of the road (in miles)
- number of days the crew has worked
- (Choose one)
- Range:
- length of the road (in miles)
- number of days the crew has worked
- (Choose one)

Transcript text: 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 $L=2 D+200$ 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. \begin{tabular}{|l|l|l|} \hline & Description of Values & Set of Values \\ \hline Domain: & \begin{tabular}{l} Olength of the road (in miles) \\ Onumber of days the crew has worked \end{tabular} & (Choose one) \\ \hline Range: & \begin{tabular}{l} Olength of the road (in miles) \\ Onumber of days the crew has worked \end{tabular} & (Choose one) \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Identify the Domain

The domain of the function $ L = 2D + 200 $ represents the possible values of $ D $, which is the number of days the crew has worked. Since the crew can work for at most 60 days, the domain is all real numbers $ D $ such that $ 0 \leq D \leq 60 $.

Step 2: Identify the Range

The range of the function $ L = 2D + 200 $ represents the possible values of $ L $, which is the total length of the road in miles. Since $ D $ ranges from 0 to 60, we can calculate the corresponding $ L $ values:

When $ D = 0 $, $ L = 2(0) + 200 = 200 $ miles.
When $ D = 60 $, $ L = 2(60) + 200 = 320 $ miles.

Thus, the range is all real numbers $ L $ such that $ 200 \leq L \leq 320 $.

Step 3: Choose the Correct Descriptions and Sets of Values

Domain Description: The domain represents the number of days the crew has worked.
Domain Set of Values: $ 0 \leq D \leq 60 $.
Range Description: The range represents the length of the road (in miles).
Range Set of Values: $ 200 \leq L \leq 320 $.