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)?

a) Domain: [0, 3.85] Range: [0, 18.05]
b) Domain: (-[infinity], 3.85) Range: [1.9, 18.05]
c) Domain: [0, 3.85] Range: [1.9, 18.05]
d) Domain: (-[infinity], 3.85) Range: [0, 18.05]

Answer 1

The domain of the function is all real numbers, and the range is approximately [0, 18.05].

Step-by-step explanation:

The domain of a function represents the possible input values or inputs for the function. In this case, the domain for the function h(t) = -4.87t^2 + 18.75t is all real numbers. In other words, there are no restrictions on the values that t can take.

The range of a function represents the possible output values or the results that the function can produce. To find the range, we look at the graph of the function. Since the coefficient for the t^2 term of the function is negative, the graph opens downwards and the highest point occurs at the vertex. The height of the vertex gives us the maximum value that the function can take, which is the range. In this case, the vertex can be found using the formula -b/2a, where a = -4.87 and b = 18.75. Plugging in these values gives us a t-value of 1.93 seconds. Plugging this t-value back into the function gives us the maximum height, which is approximately 18.05 meters. Therefore, the range of the function h(t) is approximately [0, 18.05].