To interpret the key function of the graph for the domain interval \(9 < t < 14\), we need to analyze what this specific interval could represent based on the context given.
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If we consider the interval \(9 < t < 14\):
- This suggests that we're observing some activity starting just after 9 minutes and continuing until just before 14 minutes.
- The options to consider involve how a runner, driver, or cyclist might behave during this time.
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Based on the responses provided:
- "a runner resting for 5 minutes": This would likely imply an interval of zero activity, which typically wouldn't fit a domain that reflects ongoing progress (like running).
- "a runner sprinting at a constant rate starting at minute nine": This scenario seems plausible as it indicates an active period starting at minute nine.
- "driving a car at a constant rate for five hours": This option doesn't fit, since the interval we have is only spanning 5 minutes.
- "a cyclist taking a cool down ride at a slower constant pace": Possible, but "cool down" implies a transition towards rest rather than active engagement.
Given the context and the nature of the activities described, the most fitting scenario for the portion of the piecewise function defined by the interval \(9 < t < 14\) would be:
A runner sprinting at a constant rate starting at minute nine.
This interpretation suggests that during this time, the runner is actively sprinting without interruption.
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