To accurately interpret the key function of the graph for the domain interval \(9 < t < 14\), we need to consider the behavior of the graph in that specific interval. However, since we don't have the graph itself, we can analyze the scenarios provided.
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A runner sprinting at a constant rate starting at minute nine - This scenario suggests that the graph would be a linear segment representing the runner's speed; it implies that the runner is actively covering distance during this interval.
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A cyclist taking a cool down ride at a slower constant pace - Similar to the first scenario, this would also be represented by a linear relationship, albeit at a different constant speed, indicating low intensity compared to running.
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A runner resting for 5 minutes - If the runner is resting, the graph would likely show a horizontal line, indicating no change in distance over time, which does not reflect motion.
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Driving a car at a constant rate for five hours - This scenario suggests a prolonged duration of travel at a steady speed, which is also represented as a linear function but over a significantly longer time than a few minutes.
Given that the interval \(9 < t < 14\) is relatively short (which may indicate activity rather than rest), the most fitting scenario would be:
a runner sprinting at a constant rate starting at minute nine.
This interpretation aligns with the idea of motion during that time frame. The other options either imply rest or significantly longer durations that wouldn’t fit the specified interval of 9 to 14 minutes.
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