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?
(1 point)
Responses
driving a car at a constant rate for five hours
driving a car at a constant rate for five hours
a runner sprinting at a constant rate starting at minute nine
a runner sprinting at a constant rate starting at minute nine
a cyclist taking a cool down ride at a slower constant pace
a cyclist taking a cool down ride at a slower constant pace
a runner resting for 5 minutes
. What scenario can be represented by this portion of the piecewise function?
(1 point)
Responses
driving a car at a constant rate for five hours
driving a car at a constant rate for five hours
a runner sprinting at a constant rate starting at minute nine
a runner sprinting at a constant rate starting at minute nine
a cyclist taking a cool down ride at a slower constant pace
a cyclist taking a cool down ride at a slower constant pace
a runner resting for 5 minutes
Answers
GPT-4o mini
To interpret the key function of the graph for the domain interval \( 9 < t < 14 \), we first need to consider the context of the options provided. The different scenarios describe activities with varying rates of motion or rest.
Given that the interval \( 9 < t < 14 \) suggests a specific period during which something occurs (between 9 and 14 units of time), we look at each option:
1. **Driving a car at a constant rate for five hours:** This scenario can't directly apply to \( 9 < t < 14 \) because it implies a longer duration (5 hours) starting before 9 and continuing past 14.
2. **A runner sprinting at a constant rate starting at minute nine:** This fits well if we assume the runner starts sprinting at \( t = 9 \) and continues until \( t = 14 \). This could mean the runner is at a constant pace during that time.
3. **A cyclist taking a cool down ride at a slower constant pace:** It’s plausible for a cyclist to ride during this time at a constant pace, but it does not specifically suggest a starting point at minute 9.
4. **A runner resting for 5 minutes:** This suggests no activity during the stated interval, which contradicts the idea of a continuous function representing movement or change.
Based on this analysis, the most fitting interpretation of the function on the interval \( 9 < t < 14 \) is **"a runner sprinting at a constant rate starting at minute nine."** This scenario reflects the implication that the runner begins their activity at minute 9 and maintains a consistent pace for the duration until minute 14.
Given that the interval \( 9 < t < 14 \) suggests a specific period during which something occurs (between 9 and 14 units of time), we look at each option:
1. **Driving a car at a constant rate for five hours:** This scenario can't directly apply to \( 9 < t < 14 \) because it implies a longer duration (5 hours) starting before 9 and continuing past 14.
2. **A runner sprinting at a constant rate starting at minute nine:** This fits well if we assume the runner starts sprinting at \( t = 9 \) and continues until \( t = 14 \). This could mean the runner is at a constant pace during that time.
3. **A cyclist taking a cool down ride at a slower constant pace:** It’s plausible for a cyclist to ride during this time at a constant pace, but it does not specifically suggest a starting point at minute 9.
4. **A runner resting for 5 minutes:** This suggests no activity during the stated interval, which contradicts the idea of a continuous function representing movement or change.
Based on this analysis, the most fitting interpretation of the function on the interval \( 9 < t < 14 \) is **"a runner sprinting at a constant rate starting at minute nine."** This scenario reflects the implication that the runner begins their activity at minute 9 and maintains a consistent pace for the duration until minute 14.