Question

Officials in a town use a function to analyze traffic patterns. The function uses the rate of traffic through an intersection where the domain represents the number of observed vehicles in a specified time interval. What would be the most appropriate domain for the function?

a. (... -2, -1, 0, 1, 2, 3, ...))

b. (-2, -1, 0, 1, 2, 3)

c. (0, 1/2, 1, 3/2, 2, 5/2)

d. (0, 1, 2, 3, …)

Answer 1

The most appropriate domain for the traffic patterns function would be (0, 1, 2, 3, ...).Thus the correct option is D.

Step-by-step explanation:

For a function that analyzes traffic patterns based on the rate of traffic through an intersection, the domain should represent the possible values for the number of observed vehicles in a specified time interval. In this context, the number of vehicles cannot be negative or fractional, as it doesn't make sense to have a negative count of vehicles, and the count is typically a whole number.

Option d) (0, 1, 2, 3, ...) represents a set of non-negative integers, which aligns with the practical constraints of counting vehicles. The ellipsis (...) indicates that the sequence continues indefinitely. This domain captures the essence of counting vehicles where only whole numbers are relevant. Options a), b), and c) include negative values or fractions, which are not meaningful in the context of counting observed vehicles.

In conclusion, the most appropriate domain for the function analyzing traffic patterns is option d), as it includes only non-negative whole numbers, which are realistic and applicable when quantifying the number of vehicles passing through an intersection in a given time interval.

Answer 2

The most appropriate domain for the function representing traffic patterns would be (d) (0, 1, 2, 3, ...).

Step-by-step explanation:

In the context of traffic patterns, the domain represents the number of observed vehicles, and this domain should consist of non-negative whole numbers since the number of vehicles cannot be negative or fractional. Option (d) (0, 1, 2, 3, ...) represents a sequence of non-negative integers, making it the most appropriate domain for the function analyzing traffic patterns.

Options (a) (... -2, -1, 0, 1, 2, 3, ...)), (b) (-2, -1, 0, 1, 2, 3), and (c) (0, 1/2, 1, 3/2, 2, 5/2) include negative numbers or fractional values in the domain, which may not be meaningful in the context of counting observed vehicles in a specified time interval. Therefore, option (d) is the most suitable domain for the given scenario.