Question

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. Rounded to the nearest hundredth, what are the domain and range of the function h(t)?

Answer 1

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]
 Answer:
 Domain: [0, 3.85]
 Range: [0, 18.05]
 option 1