The formula t=h√4

Question

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)
Responses

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 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.
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.

The 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 domain is h≤0
, This means that heights less than or equal to 0, or only negative heights, are being studied.

Answer 1

The correct response is:

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.

Explanation:

1. The function \( t = h\sqrt{4} \) simplifies to \( t = 2h \), which is a linear function. The relationship between height \( h \) and time \( t \) is directly proportional, meaning as height increases, time increases linearly, rather than at an increasing rate.

2. The statement about the minimum point at (0,0) is inaccurate because at zero height, the time to fall is zero, not 100 seconds.

3. The domain of this function is \( h \geq 0 \) since height cannot be negative in this context, so the statement about the domain being \( h \leq 0 \) is incorrect.

Overall, the key features of the function indicate that while the time to fall increases as height increases, it does so at a constant rate due to the linear nature of the function.