The function h(t) = -4.9t² + 19.6t is used to model the height of an object projected in the air where h(t) is the height (in meters) and t is the time (in seconds). what is the domain and range?

Mathematically, t can take any value, so the domain would be R.
In reality (physics), I would expect t≥0.

Mathematically, the range is h≤98/5, and will become infinitely negative.
In reality, h is probably ≥0, making the range 0 ≤ h ≤ 98/5.

So it depends on whether you want to take the real-world limitations into account. Seen as how they are mentioned in the question prominently, I would do so.