Question

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
A. A runner resting for 5 minutes
B. Driving a car at a constant rate for 5 hours
C. A cyclist taking a cooldown ride at a slower constant pace
D. A runner sprinting at a constant rate starting at minute 9

Answer 1

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.

- **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.

- **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.

- **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.

- **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.