Question

The function — 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.

Answer 1

The answer choice which represents the domain and range of the function h(t) as given in the task content in which case, values are rounded to the nearest hundredth is; Domain: [0, 3.85] and Range: [0, 18.05].

What are the domain and range of the function as given in the task content?

It follows from convention that the domain of a function simply refers to the set of all possible input values for that function.

Also, the range of a function is the set of all possible output values for such function.

On this note, by observing the graph in the attached image, it follows that the Domain of the function in discuss is; [0, 3.85].

While the range is the difference between the minimum and maximum height attained and can be computed as follows;

At minimum height, t = 0; hence, h(t) = 0.

At maximum height; h'(t) = 0 where h'(t) = h'(t)=-9.74t+18.75 and hence, t = 1.92.

Hence, h(1.92) = 18.05.

The range is therefore; [0, 18.05].

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