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 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
domain:	∘ number of days the crew has worked ∘ length of the road (in miles)	select
range:	∘ number of days the crew has worked ∘ length of the road (in miles)	select

Explanation:

Step1: Understand Domain and Range

Domain is the set of input values (independent variable), here \( D \) (days worked). Range is the set of output values (dependent variable), here \( L \) (road length).

Step2: Domain Description

Domain values are the number of days worked (\( D \)). The crew works at most 70 days, so \( D \) is from 0 to 70 (inclusive), non - negative integers or real numbers (since days can be a fraction in theory, but here probably integers from 0 to 70).

Step3: Range Description

Range values are the length of the road (\( L = 4D+400 \)). When \( D = 0 \), \( L=400 \); when \( D = 70 \), \( L=4\times70 + 400=280 + 400 = 680 \). So \( L \) ranges from 400 to 680 (inclusive) as \( D \) ranges from 0 to 70.

Answer:

• Domain:
• Description of Values: number of days the crew has worked
• Set of Values: \( 0\leq D\leq70 \) (where \( D \) is a real number or integer representing days)
• Range:
• Description of Values: length of the road (in miles)
• Set of Values: \( 400\leq L\leq680 \) (where \( L = 4D + 400\) and \( 0\leq D\leq70\))