Which domain corresponds to the described function:
The function represents the velocity of a stone after being dropped from a great height as a function of time.
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Which domain corresponds to the described function:
The function represents the velocity of a stone after being dropped from a great height as a function of time.
According to logic, the speed of the stone during a fall from a great height will increase as it falls with acceleration.
In other words, the speed of the stone increases, so the appropriate domain for this function is - always increasing.
Always increasing
Is the function in the graph decreasing?
Gravity acts as a constant force pulling the stone downward! Unlike moving at steady speed on flat ground, falling objects accelerate at 9.8 m/s² every second.
Great question! With significant air resistance, velocity would eventually reach a terminal velocity and level off. But this problem assumes ideal conditions with negligible air resistance.
If thrown upward, velocity would first decrease (slowing down going up), reach zero at the peak, then increase while falling down. This problem specifies the stone is dropped, so it only falls.
The rate of increase stays the same regardless of height (9.8 m/s²), but dropping from greater height means more time to accelerate, reaching higher final speeds.
A function is always increasing when its output values get larger as the input increases. Here, as time passes (input), velocity gets faster (output grows).
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