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 70 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: <br> ∘ number of days the crew has worked <br> ∘ length of the road (in miles)	select <br> ↓

Explanation:

Step1: Define domain variable

The domain represents the input of the function, which is the number of days worked ($D$). The crew can work at most 70 days, and cannot work negative days, so:
$0 \leq D \leq 70$

Step2: Define range variable

The range represents the output of the function, which is the total length of the road ($L$). Use the given formula $L=3D+200$ to find the minimum and maximum values:
Minimum $L$ (when $D=0$): $L=3(0)+200=200$
Maximum $L$ (when $D=70$): $L=3(70)+200=210+200=410$
So:
$200 \leq L \leq 410$

Answer:

Domain:

Description of Values: $\boldsymbol{\text{number of days the crew has worked}}$
Set of Values: $\boldsymbol{0 \leq D \leq 70}$

Range:

Description of Values: $\boldsymbol{\text{length of the road (in miles)}}$
Set of Values: $\boldsymbol{200 \leq L \leq 410}$