The function f(x) = –0.5x2 + 16x – 96 can be used to trace the path of a rocket, where the x-axis represents the ground and the y-axis measures the height of the rocket. the mathematical domain of the function is all real numbers. the reasonable domain of the function is when 8 ≤ x ≤ x greater than or equal to eight but less than or equal to what value?

8 ≤ x ≤ 24

x greater than or equal to eight but less than or equal to 24

Step-by-step explanation:

Since the height can be negative, the reasonable domain will occur when f(x) = 0. In other words, the reasonable domain lies in the interval when the rocket is launched (height = 0) and the rocket returns to the ground (again, height = 0)

Now, to find the reasonable domain, we just need to replace f(x) with 0 and solve for :

Using a graphing calculator, attached picture, we get that when and and .

We can conclude that the reasonable domain of our function is  x greater than or equal to eight but less than or equal to 24