Question

A rocket is shot straight up into the air. If f(t) represents the height in feet of the rocket at time, t, seconds and g(t) is a constant function that represents the height of a platform, what situation can be described by (f+g)(t)? Include a description of the domain of (f+g)(t).
Make it simple in one paragraph and like a kid wrote it.

Answer 1

Imagine a rocket that goes really high up into the sky, and it's being launched from a platform that is already high above the ground, like on a tall building. The function f(t) tells us how high the rocket is at any moment in time, t, and the function g(t) is just the height of the platform, which stays the same because it's a constant. When we add f(t) and g(t) together to get (f+g)(t), we're finding out the total height of the rocket above the ground at any time. So, if you want to know how high the rocket really is from the ground, you just use (f+g)(t). The domain of (f+g)(t) is all the times t when the rocket is in the air, starting from when the rocket is launched until it falls back down, which is usually from t = 0 seconds to when it lands, but it can't be a negative time because that doesn't make sense!