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Question

A piecewise linear function consisting of three parts is plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Time in minutes, and the y-axis is labeled Distance in miles.

Interpret the key function of the graph for the domain interval 9<t<14. What scenario can be represented by this portion of the piecewise function?

(1 point)
Responses

a cyclist taking a cool down ride at a slower constant pace
a cyclist taking a cool down ride at a slower constant pace

a runner sprinting at a constant rate starting at minute nine
a runner sprinting at a constant rate starting at minute nine

driving a car at a constant rate for five hours
driving a car at a constant rate for five hours

a runner resting for 5 minutes
a runner resting for 5 minutes

Answer 1

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.