what is the domain and range of this function h(t)=−16t2+98t

Answer 1

The domain of a function is the set of all possible input values, while the range is the set of all possible output values.

For the function h(t) = -16t^2 + 98t, the domain can be any real number because there are no restrictions on the input variable t.

To find the range, we need to determine the possible values of h(t).

The function is in the form of a quadratic equation, where the coefficient of the t^2 term is negative (-16). This means that the graph of the function opens downward, and the maximum value occurs at the vertex.

The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a = -16 and b = 98.

Plugging in the values, we get:
x = -98/(2*(-16)) = 98/32 ≈ 3.063.

Since the graph opens downward, the vertex represents the maximum point of the parabola. Thus, the maximum value of h(t) is the output value of the vertex.

To find the maximum value, we substitute the x-coordinate of the vertex back into the original function: h(3.063) = -16(3.063)^2 + 98(3.063) ≈ 149.521.

Therefore, the range of the function h(t) = -16t^2 + 98t is (-∞, 149.521].