Question

For the function h(t) = -4.87t^2 + 18.75, determine the domain and range.

Domain of h(t):
A) All real numbers
B) t ≥ 0
C) t ≤ 0
D) t is an integer

Answer 1

The domain of the function h(t) is all real numbers, and the range is t ≤ 18.75.

Step-by-step explanation:

The function h(t) = -4.87t^2 + 18.75 is a quadratic function, which means it is defined for all real numbers. Therefore, the domain of h(t) is A) All real numbers.

To determine the range of the function h(t), we need to look at the coefficient of the t^2 term, which is -4.87. Since this coefficient is negative, the parabola opens downward. The vertex of the parabola is the highest point on the graph, so the range of h(t) is all real numbers less than or equal to the y-coordinate of the vertex.

The equation of the vertex can be found using the formula t = -b / (2a). For h(t), a = -4.87 and b = 0. Using these values in the formula, we find that t = 0. Then, substituting t = 0 into the function h(t), we get h(0) = 18.75.

Therefore, the range of the function h(t) is t ≤ 18.75.