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 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.
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 the time it takes an object to fall to the ground is increasing and is increasing at an increasing rate.

Answer 1

The key features of the function \( t = h\sqrt{4} \) can be analyzed as follows:

1. Increasing Function: The function is indeed an increasing function. Since \( \sqrt{4} = 2 \), the formula simplifies to \( t = 2h \). As the height \( h \) increases, the time \( t \) also increases linearly, which means it increases at a constant rate rather than not at a constant rate.

2. Minimum Point: The minimum point of the function is at \( (0, 0) \). This indicates that when the height \( h \) is 0 feet, the time \( t \) it takes for the object to fall to the ground is also 0 seconds, not 100 seconds.

3. Domain: The domain of this function is \( h \geq 0 \), not \( h \leq 0 \). This means that only positive heights (including zero) are being studied, as negative heights do not have physical relevance in this context.

4. Rate of Increase: The function \( t = 2h \) shows a linear relationship between height and time. Thus, the time it takes for an object to fall increases at a constant rate of 2 seconds per foot of height.

So, only the first statement captures some degree of the increasing behavior, even though it mentions that it does not increase at a constant rate, which is incorrect in this context as it does increase at a constant rate. None of the other statements accurately describe the function based on the features mentioned.

To summarize:

• The correct interpretation would be that the function is linear and increasing at a constant rate, with \( t \) being 0 when \( h = 0 \), and the domain should be \( h \geq 0 \).