Question
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An item is being lifted by an elevator at a constant speed to a height of 10 feet. The item does not move for five seconds then catapults off the 10 -foot platform and back to the ground. Compare the height of the item to the time passed in seconds. Determine the correct types of functions that describes the scenario in the correct order. ( 1 point) Linear Function, Constant Function, Linear Function Linear Function, Constant Function, Quadratic Function Constant Function, Quadratic Function, Linear Function Quadratic Function, Constant Function, Linear Function

Ask by Luna Rojas. in the United States
Mar 12,2025

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Answer

The correct order of functions is: Linear Function, Constant Function, Quadratic Function

Solution

1. During the elevator phase, the item is moving upward at a constant speed, so its height as a function of time can be described by a linear function, e.g., \( h(t) = mt + b \). 2. When the item is stationary on the 10-foot platform for five seconds, its height remains constant. Thus, the height is described by a constant function, e.g., \( h(t) = 10 \). 3. When the item catapults off the platform and falls back to the ground, its motion under gravity is described by a quadratic function, e.g., \( h(t) = at^2 + bt + c \). The correct order is: \( \textbf{Linear Function, Constant Function, Quadratic Function} \).

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Bonus Knowledge

This scenario can be understood as a series of movements. Initially, while the elevator lifts the item at a constant speed to the height of 10 feet, the height versus time is represented by a linear function. Once the item reaches the 10-foot height and remains there for five seconds, the height is constant, thus described by a constant function. When the item is catapulted off the platform, it enters a trajectory back to the ground, which is a parabola or quadratic function as the height decreases over time. Putting these observations together, the correct order is: Linear Function (ascending), Constant Function (flat for 5 seconds at 10 feet), Quadratic Function (descending as it falls to the ground). Hence, the right answer is: Linear Function, Constant Function, Quadratic Function.

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