To interpret the key function of the graph for the domain interval \( 9 < t < 14 \), we need to understand the nature of the graph in question. Since we don't have the actual graph, we will rely on the options provided to deduce the most appropriate scenario.
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Option A: A runner resting for 5 minutes. This suggests that the function would be flat over that interval, indicating zero movement, which would typically be represented by a constant value.
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Option B: Driving a car at a constant rate for 5 hours. This implies a linear function with a constant positive slope, indicating that the distance is increasing steadily, which doesn't align with a time interval of 5 units unless specified that the units are hours.
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Option C: A cyclist taking a cooldown ride at a slower constant pace. This suggests that the function might also be linear but at a positive but low slope, indicating that there is movement, albeit at a reduced speed.
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Option D: A runner sprinting at a constant rate starting at minute 9. This would be a sharp linear increase, indicating the runner is starting to move faster at minute 9 and continuing to do so.
Given that the question specifies the interval \( 9 < t < 14 \), if the function represents activity during this time (meaning the speed is constant and above zero), it implies movement.
In this situation, the most fitting answer would be: C. A cyclist taking a cooldown ride at a slower constant pace.
This represents a scenario where the cyclist is moving, but at a slower pace, fitting within the structure of a function that could be defined as constant over that interval.
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