Question

The function f(t) = 7.2t + 5 models the average distance, f(t), in kilometers that Bob rides his bike over time, t, in hours.

The function g(t) = 5.9 + 10 models the average distance, g(t), in kilometers that Alice walks over time, t, in hours.
What are the domains of the two functions?
a) All real numbers
b) t < 0
c) t > 0
d) 0 < t < [infinity]

Answer 1

The domains of the functions f(t) = 7.2t + 5 and g(t) = 5.9t + 10, which model distance over time, are all non-negative real numbers, since time cannot be negative. Hence, the correct domain is 0 < t < [infinity].

Step-by-step explanation:

The domain of a function refers to the set of possible input values (usually t for time) for which the function is defined. For the functions f(t) = 7.2t + 5 and g(t) = 5.9t + 10 that model the average distance traveled by Bob and Alice over time, the domain would logically be all non-negative real numbers. This is because time cannot be negative in this context. Therefore, the correct answer is d) 0 < t < [infinity].

It's worth noting that there may be practical or physical restrictions on the domain in real-world situations, but mathematically, the domain includes all non-negative times for continuous functions such as these that model distances over time.