To interpret the key function of the graph in the interval \(9 < t < 14\), we can analyze the characteristics of the graph represented in this domain. Since it is a piecewise linear function in quadrant 1, we are likely observing a scenario that involves moving or changing distance over time.
Given the response options, the most fitting scenario for the interval \(9 < t < 14\) would likely be related to a consistent activity such as running or cycling. A piecewise function that is linear suggests a constant rate of distance covered over time.
Among the options provided, the response "a runner sprinting at a constant rate starting at minute nine" aligns with the characteristics of a linear function implied in the mentioned interval. This response indicates that the runner maintains a steady speed during those minutes instead of resting or slowing down.
Therefore, the correct interpretation of the interval \(9 < t < 14\) is:
a runner sprinting at a constant rate starting at minute nine.