Question

A potato was launched in the air using a potato gun. The function for the situation was h(t) =-16t^2 + 100t + 10, where t was the time in seconds and h(t) was the height in feet. What are the domain and range of the function, as they apply to the actual path of the potato?

Answer 1

The domain of the function h(t) is all positive values of t, while the range is all values less than or equal to 289.0625 feet.

Step-by-step explanation:

The domain of the function h(t) is all possible values of t that make sense in the context of the problem. In this case, since we are dealing with time, the domain should be all positive values of t. The range of the function h(t) is all possible values of h(t) that the potato can achieve as it is launched into the air. To find the range, we can consider the vertex of the parabolic function. The vertex can be found using the formula t = -b/2a = -100/-32 = 3.125. So, the highest point the potato can reach is at t = 3.125 seconds. Substituting this value in the function, we can find the maximum height:

h(3.125) = -16(3.125)^2 + 100(3.125) + 10 = 289.0625 feet.

Therefore, the domain of the function h(t) is all positive values of t, while the range is all values less than or equal to 289.0625 (since the height cannot be negative).

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