The function h(t)= -4.87t^2+18.75t is used to model the height of an object projected in the air, where h(t) is the height in meters and t is the time in seconds. What are the domain and range of the function h(t)? Round values to the nearest hundredth

[tex]The function h(t)= -4.87t^2+18.75t is used to model the height of an object projected in the air, w[/tex]

Looking at the graph you can see that the domain of the function is:

[0, 3.85]

To find the range of the function, we must follow the following steps:

Step 1)

Evaluate for t = 0

h (0) = - 4.87 (0) ^ 2 + 18.75 (0)

h (0) = 0

Step 2)

find the maximum of the function:

h (t) = - 4.87t ^ 2 + 18.75t

h '(t) = - 9.74 * t + 18.75

-9.74 * t + 18.75 = 0

t = 18.75 / 9.74

t = 1.925051335

We evaluate the function at its maximum point:

h (1.925051335) = - 4.87 * (1.925051335) ^ 2 + 18.75 * (1.925051335)

h (1.93) = 18.05

The range of the function is:

[0, 18.05]

Domain: [0, 3.85]

Range: [0, 18.05]

option 1

A.domain: [0, 3.85]

range: [0, 18.05]

Step-by-step explanation:

Domain: t≥0

Range:h(t) ≤ 0.85

Step-by-step explanation:

The domain of a function is all the valid values you can enter into the function. Because time can't be negative the domain is t>0. The range or h(t) is the result, because the object can't go through the ground, it can't be less than zero. 0≤h(t)

0≤-4.87t^2+18.75t

0≤-4.87t+18.75

-18.75≤-4.87t

which is approx.: 0.85≥t or t≤0.85

The correct answer is the first choice.

For the domain, we are looking at the included x-values. The values go from 0 to about 3.85.

For the range, we are looking at the included y-values. The values go from 0 to the top height of about 18.05.