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+400) 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
range:	number of days the crew has worked<br>length of the road (in miles)	select

Explanation:

Step1: Define domain and range concepts

Domain is the set of input values (independent variable), range is the set of output values (dependent variable). Here, the function is $L = 4D+400$, where $D$ is the number of days and $L$ is the length of the road.

Step2: Identify domain

The independent variable is the number of days $D$ the crew has worked. So the description of the domain values is "number of days the crew has worked". The crew can work for at most 60 days and the number of days $D\geq0$. So the set of values for the domain is $\{D|0\leq D\leq60, D\in\mathbb{Z}\}$ (assuming $D$ is an integer - number of days).

Step3: Identify range

The dependent variable is the length of the road $L$. So the description of the range values is "length of the road (in miles)". When $D = 0$, $L=4\times0 + 400=400$. When $D = 60$, $L=4\times60+400=240 + 400=640$. So the set of values for the range is $\{L|400\leq L\leq640, L\in\mathbb{R}\}$ (since length can be a real - valued quantity).

Answer:

Domain:

• Description of Values: number of days the crew has worked
• Set of Values: $\{D|0\leq D\leq60, D\in\mathbb{Z}\}$

Range:

• Description of Values: length of the road (in miles)
• Set of Values: $\{L|400\leq L\leq640, L\in\mathbb{R}\}$