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 = 3d + 200 gives l as a function of d. the crew can work for at most 80 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 | select | | range: | ∘ length of the road (in miles) ∘ number of days the crew has worked | select |

Explanation:

Step1: Define domain (input variable)

The domain is the set of all valid input values for the function. Here, the input variable is $D$, which represents the number of days worked. The crew can work 0 to at most 80 days, so the domain values are non-negative integers (or real numbers) from 0 to 80.

Step2: Define range (output variable)

The range is the set of all valid output values. The output is $L=3D+200$. Substitute the minimum and maximum $D$ values:
When $D=0$, $L=3(0)+200=200$
When $D=80$, $L=3(80)+200=440$
So the range values are from 200 to 440 miles.

Answer:

Domain:

Description of Values: number of days the crew has worked
Set of Values: $0 \leq D \leq 80$ (where $D$ is a non-negative integer or real number representing days)

Range:

Description of Values: length of the road (in miles)
Set of Values: $200 \leq L \leq 440$ (where $L$ is the length of the road in miles)