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 = 4d + 200 ) gives ( l ) as a function of ( d ). the crew can work for at most 90 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

| | domain:

• number of days the crew has worked
• length of the road (in miles)

|
| | range:

• number of days the crew has worked
• length of the road (in miles)

|
| | set of values

• select

|
| | set of values

• select

|

Explanation:

Step1: Define domain description

The domain is the input variable $D$, which represents the number of days the crew has worked.

Step2: Find domain value set

The crew can work 0 to at most 90 days, so the domain is all integers from 0 to 90, or $0\leq D\leq90$ where $D$ is a non-negative integer.

Step3: Define range description

The range is the output variable $L$, which represents the length of the road (in miles).

Step4: Calculate range value set

Substitute the domain bounds into $L=4D+200$:
When $D=0$, $L=4(0)+200=200$
When $D=90$, $L=4(90)+200=360+200=560$
So the range is $200\leq L\leq560$ where $L$ is an integer (since $D$ is integer, $L$ will be integer).

Answer:

Domain:

Description of Values: Number of days the crew has worked
Set of Values: All integers from 0 to 90 (or $0\leq D\leq90$, $D\in\mathbb{Z}_{\geq0}$)

Range:

Description of Values: Length of the road (in miles)
Set of Values: All integers from 200 to 560 (or $200\leq L\leq560$, $L\in\mathbb{Z}_{\geq0}$)