Final answer:
The most appropriate domain for a graph showing an airplane's altitude over time is '{t: t > 0 min}', indicating that time is recorded in minutes and starts from the moment of takeoff. Altitude is dependent on the passage of time and the graph's domain includes only positive time values after the plane’s takeoff.The correct option is option b.
Step-by-step explanation:
The question is about determining the most appropriate domain for a graph that illustrates an airplane's altitude as a function of time since takeoff. In the context of this question, the domain represents all the possible values that time (t) can take. Altitude is typically measured from the point of takeoff, so the domain would not include negative time values or measurements that are not time-related.
Considering the options provided, the most appropriate domain for this graph would be '{t: t > 0 min}' or option B. This choice represents time values greater than zero, which makes sense as a plane's altitude is only relevant after it has begun to take off. The units 'minutes' are more practical for flight duration than 'seconds'. Option A is also a correct domain but is less practical, option C includes days which is improbable for a continuous flight, and option D is irrelevant because it specifies a range of altitudes, not a range of time.
It's important to understand that in a position vs. time graph, the position typically is on the vertical axis, with time on the horizontal axis. The slope of the graph would indicate the velocity of the airplane if we assume a constant acceleration of zero.