8. Officials in a town use a function, C, to analyze traffic patterns. \( C(n) \) represents the rate of traffic through an intersection where \( n \) is the number of observed vehicles in a specific time interval. What would be the most appropriate domain for the function? a. \( \{\ldots-2,-1,0,1,2,3, \ldots\} \) b. \( \{-2,-1,0,1,2,3\} \) c. \( \left\{0, \frac{1}{2}, 1,1 \frac{1}{2} 2,2 \frac{1}{2}\right\} \) d. \( \{0,1,2,3, \ldots\} \)

The most appropriate domain for the function \(C(n)\) is \( \{0, 1, 2, 3, \ldots\} \). This set includes all non-negative integers, which makes perfect sense! After all, you can’t have a negative count of vehicles – so \(n\) must be zero or a positive integer, reflecting the actual number of observed vehicles. Traffic analysis is a critical component of urban planning and transportation management. Using this function, officials can effectively monitor and optimize traffic flow. The data collected can inform traffic light patterns, road construction decisions, or public transportation routes, improving overall travel efficiency and safety for everyone on the road!