The maximum walking speed (in feet per second) of a large animal can be modeled by the equation S = sqrt(gL) where S = speed in feet per second, g = a constant rate of 32 feet per second, and L = the length of one leg of the animal, in feet.

What domain makes sense for the function S(L) = sqrt(gL)

A. L is any real number
B. 0 < L <= 32

D. L >= 32

What range makes sense for the function S(L) = sqrt(gL)?

A. 0 < S <= 32
B. S => 32

D. S is any real number

Please help me!! And thank you :)

since √x is defined only for x≥0, you need gL= 32L ≥ 0

That is L≥0

for the range, since gL ≥ 0, S ≥ 0

where is choice C for both questions?
ever hear of proofreading?

there is but I knew that answer was wrong, I took the c out

To determine the domain and range for the function S(L) = sqrt(gL), let's analyze the variables involved.

Domain:
The length of one leg, L, must be a non-negative value because length cannot be negative in this context. Additionally, since S(L) represents the maximum walking speed, it is reasonable to assume that the animal must have at least one leg, meaning L cannot be zero. Therefore, the domain for the function should be L > 0.

Looking at the given options, we can see that:

Option A. L is any real number - This includes negative values for L, which does not make sense in this context.

Option B. 0 < L <= 32 - This option restricts L to be between 0 and 32, which is not a valid range because it limits the leg length based on a specific value.

Option D. L >= 32 - This option allows L to be any value greater than or equal to 32. It does not restrict the range of L unnecessarily and fits the context of the problem well. Therefore, option D is the correct choice for the domain.

Regarding the range:

The function S(L) = sqrt(gL) represents the maximum walking speed, which can be any positive value. Since the square root of a positive number is always positive, the range for S(L) should also be any positive value.

Looking at the given options:

Option A. 0 < S <= 32 - This option restricts the range of S to be between 0 and 32, which is not appropriate considering the function can output values greater than 32.

Option B. S >= 32 - This option suggests that the speed should be greater than or equal to 32. However, the function can output values less than 32, especially for small leg lengths.

Option D. S is any real number - This option includes all possible values for speed, covering both positive and negative values. However, since the speed of an animal cannot be negative, this option is not suitable.

Therefore, the correct choice for the range is option D, which states that S can take any positive real number as its values.

In summary, the correct choices are:

Domain: D. L >= 32
Range: D. S is any real number (specifically, any positive real number).