Question

The function h(t) = -4.878 + 18.754 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.

A. Domain: (-[infinity], [infinity]), Range: (-[infinity], [infinity])
B. Domain: (1.9, 13), Range: (18.05, 10)
C. Domain: (0, [infinity]), Range: (-[infinity], [infinity])
D. Domain: (-[infinity], [infinity]), Range: (1.9, 13)

Answer 1

The domain of the function h(t) is (-∞, ∞) and the range is (13.88, 13.88).

Step-by-step explanation:

The domain of a function refers to the set of all possible inputs or values that the independent variable can take. In this case, the independent variable is time, denoted by t. Since time can take on any value, the domain of the function h(t) is (-∞, ∞). So, the correct option for the domain is A.

The range of a function refers to the set of all possible outputs or values that the dependent variable can take. In this case, the dependent variable is height, denoted by h(t). From the given function, we can see that the height is always -4.878 + 18.754, which simplifies to a constant value of 13.876. So, the range of the function h(t) is (13.876, 13.876). Rounded to the nearest hundredth, the range is (13.88, 13.88). Therefore, the correct option for the range is D.