Answer:
1) The function is monotonically increasing
2) The end behavior of the function is x tends to infinity as t(x) tends infinity
3) The x and y -intercept is (0, 0)
4) The endpoint is (0, 0)
5) The domain is 0 ≤ x ≤ +∞
The range is 0 ≤ t(x) ≤ +∞
Step-by-step explanation:
1) The given function of the time for the object to hit the ground is t(x) = 1/4·√x
Where;
x = The distance from the ground
t = The time it takes for the object to hit the ground
Monotonically increasing function, we have;
A function that is continuous on [a, b] and it can be differentiated in the domain, (a, b) is monotonically increasing when df(x)/dx > 0 for all values of x in (a, b)
However, where df(x)/dx < 0 for all values of x in (a, b), the function is decreasing
Therefore, using an online tool, we have;
dt(x)/dx = d(1/4·√x)/dx = 1/8 × 1/√x
Therefore, the dt(x)/dx > 0, for 0 < x < +∞ and the function is monotonically increasing
2) The end behavior of the function as x tends to infinity, t(x) = 1/4·√x approaches infinity
3) From the end behavior, and the nature, of the function t(x) = 1/4·√x, where both variables are directly proportional, we have that the x and y -intercept = (0, 0)
4) The endpoint is (0, 0) given that as t(x) tends to 0, x tends to 0
5) The domain is 0 ≤ x ≤ +∞
The range is 0 ≤ t(x) ≤ +∞.
