Use the image to answer the 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 runner sprinting at a constant rate starting at minute nine
a runner sprinting at a constant rate starting at minute nine

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

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

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

1 answer

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.