Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a specific input value into a function to determine its output. In this context, f(t) and g(t) represent the distance from the car at different times, so evaluating f(0) and f(2) gives the distances at the start and end of the hike to the lake, while g(0) and g(2) provide the distances at the start and end of the return hike.
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Piecewise Functions
Piecewise functions are defined by different expressions based on the input value. In this scenario, f(t) and g(t) can be considered piecewise because they describe different segments of the journey: f(t) for the hike to the lake and g(t) for the return trip. Understanding how to interpret these functions is crucial for evaluating them correctly.
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Distance and Time Relationship
The relationship between distance and time is fundamental in calculus, particularly in motion problems. Here, the distance from the car changes over time as the hiker moves towards the lake and back. Recognizing that the total distance is constant (3 miles) and how it is divided over the two hikes helps in understanding the function's behavior and evaluating it accurately.
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