To interpret the portion of the piecewise function for the domain interval \(9 < t < 14\), we need to consider what the graph indicates regarding distance traveled during that time frame.
If this interval represents a straight, horizontal line on the graph, it would suggest that the distance is constant, meaning the cyclist or runner is not changing their pace or speed. This would correspond to a scenario where the person is taking a rest or maintaining a constant speed.
Given the provided options, it seems that "a runner resting for 5 minutes" is the most appropriate interpretation for the interval \(9 < t < 14\) if the graph shows constant distance (no increase) during that time.
If the line was sloping upwards, it could suggest someone moving at a constant pace, which could relate to the scenario of a cyclist or runner, but based on the options given and the context of "rest" seems to be the best fit.
Therefore, the correct response would be:
a runner resting for 5 minutes.