The function h (t) = - 16t2+144 represents the height, h (t), in feet, of an object from the ground at t second after its dropped. A realistic domain for this function is

The domain is the limits of the function. Since time doesnt go negative, start with 0. At time 0, the height is

-16 (0) ^2 + 144 = 144ft

Then, solve for t to find the upper limit for t, which is when the height is zero (since you're dropping the object).

-16t^2 + 144 = 0

-16t^2 = - 144

t^2 = 9

t = sqrt (9)

t = 3

The domain is 0 to 3 seconds.