The function h (t) = - 16t * 2 + 144 represents the height, h (t), in feet, of an object from the ground at t seconds after it is dropped. A realistic domain for this function is ...

1) - 3 <_ t <_ 3

2) 0 <_ t <_ 3

3) 0 <_ h (t) <_ 144

4) all real numbers

The realistic domain of the function is 0 ≤ t ≤ 3 ⇒ answer (2)

Step-by-step explanation:

- The function h (t) = - 16t² + 144 represents the height, h (t), in feet, of an

object from the ground at t seconds after it is dropped

∵ h (t) = - 16t² + 144

∵ At the beginning t = 0

- Substitute the value of t in the function

∴ h (0) = - 16 (0) ² + 144

∴ h (0) = 144

* The object was on a height 144 when t = 0

* Lets find the time when the object reached the ground

- When the object reached the ground its height = 0

∵ h (t) = - 16t² + 144

∵ h = 0

- Substitute the value of h in the function

∴ 0 = - 16t² + 144

- Add 16t² to both sides

∴ 16t² = 144

- Divide both sides by 16

∴ t² = 9

- Take √ for both sides

∴ t = 3 seconds

* The object reached the ground after 3 seconds

∵ The domain of the function is the values of t

∴ The realistic domain of the function is 0 ≤ t ≤ 3