Question

The formula t=h√4 can be used to estimate the time in seconds it takes an object at a height of h feet to fall to the ground.What do the key features of the function reveal?(1 point)ResponsesThe minimum point is at (0,0). This point indicates that when the height of the object is 0 feet, the time it takes the object to fall to the ground is 100 seconds.The minimum point is at  open paren 0 comma 0 close paren . This point indicates that when the height of the object is 0 feet, the time it takes the object to fall to the ground is 100 seconds.The function is an increasing function, so the time it takes an object to fall to the ground is increasing and is increasing at an increasing rate.The function is an increasing function, so the time it takes an object to fall to the ground is increasing and is increasing at an increasing rate.The domain is h≤0, This means that heights less than or equal to 0, or only negative heights, are being studied.The domain is h is less than or equal to 0 , This means that heights less than or equal to 0, or only negative heights, are being studied.The function is an increasing function, so as the height of the object increases, the time it takes the object to fall to the ground increases but not at a constant rate.

Answer 1

Analyzing the function \( t = h\sqrt{4} \), we can derive some key features and insights. Let's clarify the statements given in your question:

1. **Minimum Point**: The statement that the minimum point is at (0,0) is inaccurate in the context provided. When \( h = 0 \), \( t = 0 \) which means if there is no height, it takes 0 seconds for the object to fall since it is already on the ground.

2. **Function Behavior**: The function \( t = h\sqrt{4} \) can be simplified to \( t = 2h \). This is a linear function implying that as height \( h \) increases, the time \( t \) to fall increases linearly; it does not increase at an accelerating rate, but rather at a constant rate.

3. **Domain**: The domain of this function should be \( h \geq 0 \) since height cannot be negative in this context. The statement indicating the domain as \( h \leq 0 \) is incorrect.

4. **Increasing Function**: Given \( t = 2h \), this function is indeed an increasing function from the domain \( h \geq 0 \) and does indicate that as height increases, the time before the object falls increases, but at a constant rate (not at an increasing rate).

Therefore, the most accurate interpretation of the features of the function \( t = 2h \) is that it is an increasing linear function. The time it takes for an object to fall increases as the height increases, and it does so at a constant rate, meaning that doubling the height would double the time. The minimum time is indeed 0 seconds when the height is 0 feet.

Here’s a refined statement regarding the function:

"The function is an increasing linear function defined for \( h \geq 0 \), which indicates that as the height of the object increases, the time it takes for the object to fall to the ground increases at a constant rate."