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. What are the domain and range of the function h(t)? Round values to the nearest hundredth.


domain: [0, 3.85]
range: [0, 18.05]
domain: (-infinity, 3.85]
range: [1.9,18.05]
domain: [0, 3.85]
range: [1.9,18.05]
domain: (infinity, 3.85]
range: [0, 18.05]

Answer 1

Correct choice: domain [0, 3.85], range [0, 18.05].

Reason: h(t)=−4.87t^2+18.75t has zeros at t=0 and t=18.75/4.87≈3.85, so physically t∈[0,3.85]. The maximum occurs at t=18.75/(2·4.87)≈1.92 with height = 18.75^2/(4·4.87)≈18.05 m, and the minimum on the domain is 0, so range [0,18.05].