The function h(t)=−16t2+98t
graphed below shows the height, in feet, of a kicked soccer ball as a function of time, in seconds.
A reasonable domain of the function is
(1 point)
Responses
{t| 2≤t≤66}
{t| 0≤t≤66}
{t| 0≤t≤4.1}
and a reasonable range of the function is (1 point)
Responses
{h|0≤h<4.1}
{h|2≤h<66}
{h|0≤h≤66}
The graph of the function h(t) = -16t^2 + 98t is a downward-opening quadratic, which means it opens downwards and has a maximum point. The domain of the function would be the set of possible values for t, which in this case would be the time in seconds. Since time cannot be negative in this context, a reasonable domain would be t ≥ 0.
The range of the function would be the set of possible values for h, which in this case represents the height of the soccer ball. Since the coefficient of t^2 is negative, the function is decreasing and will have a maximum value. The range of the function would be the values of h that are less than or equal to the maximum height of the ball. Therefore, a reasonable range would be h ≤ maximum height.
From the graph, it can be seen that the ball reaches its maximum height at t = 3. Original value: h(3)=70 m. So, maximum height is 70m.
Therefore, a reasonable domain of the function is {t | 0 ≤ t ≤ 3} and a reasonable range of the function is {h | 0 ≤ h ≤ 70}.
None of the given options match this answer.