To interpret the key function of the graph for the domain interval \(9 < t < 14\), we need to understand what the behavior of the function represents at that specific interval.
Given the options, here’s a breakdown:
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A runner sprinting at a constant rate starting at minute nine: This could fit if the graph shows a linear increase in distance over the time interval.
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A cyclist taking a cool down ride at a slower constant pace: This would apply if the graph shows a less steep line relative to the previous intervals.
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Driving a car at a constant rate for five hours: This seems unlikely since the given interval is 5 minutes (from time 9 to time 14) and driving for five hours would not fit that timeframe.
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A runner resting for 5 minutes: If the graph were flat during this interval (indicating no distance covered), this could represent a resting period.
Based on typical interpretations of piecewise functions, if the graph indicates a constant rate of change (e.g., linear), the most likely representation would be "a runner sprinting at a constant rate starting at minute nine." If it is flat (indicating no movement), the runner resting scenario would apply.
Without the actual graph, the knowledge of the domain's behavior is key. Therefore, the choice can depend on the visual representation:
- If it’s a line with positive slope: a runner sprinting at a constant rate starting at minute nine.
- If it’s a horizontal line: a runner resting for 5 minutes.
If there is any indication of slope in that graph for \(9 < t < 14\), then the best answer is: a runner sprinting at a constant rate starting at minute nine.
If the segment is flat, then opt for: a runner resting for 5 minutes.
Make sure to analyze the graph to ascertain the correct interpretation.