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 and like a kid wrote it.
Make it simple and like a kid wrote it.
Answers
GPT-4o mini
Okay! So imagine you have a rocket and it's flying up into the sky. The height of the rocket at any time is given by the function \( f(t) \), which tells us how high the rocket is.
Now, let’s say there’s a platform, like a tall building or a roof, and its height doesn't change—it's always the same. We can say its height is given by \( g(t) \), which is a constant.
When we look at \( (f + g)(t) \), we are adding the height of the rocket to the height of the platform. So this new function tells us how high the rocket is above the ground when you also think about how high the platform is.
For example, if the rocket is 100 feet high (that’s \( f(t) \)), and the platform is 50 feet high (that’s \( g(t) = 50 \)), then \( (f + g)(t) \) would tell us that the total height above ground is 150 feet!
Now, about the domain of \( (f + g)(t) \): This is just the time values we can use for our function. If we're looking at the rocket’s height over time, we usually start counting time from 0 seconds (when the rocket is launched), and we keep counting as long as the rocket is flying. So, the domain would be all the time values \( t \geq 0 \), because we can’t go back in time for this scenario.
In short, \( (f+g)(t) \) helps us understand how high the rocket is above the ground, taking into account the height of the platform, as time goes on starting from when the rocket is launched!
Now, let’s say there’s a platform, like a tall building or a roof, and its height doesn't change—it's always the same. We can say its height is given by \( g(t) \), which is a constant.
When we look at \( (f + g)(t) \), we are adding the height of the rocket to the height of the platform. So this new function tells us how high the rocket is above the ground when you also think about how high the platform is.
For example, if the rocket is 100 feet high (that’s \( f(t) \)), and the platform is 50 feet high (that’s \( g(t) = 50 \)), then \( (f + g)(t) \) would tell us that the total height above ground is 150 feet!
Now, about the domain of \( (f + g)(t) \): This is just the time values we can use for our function. If we're looking at the rocket’s height over time, we usually start counting time from 0 seconds (when the rocket is launched), and we keep counting as long as the rocket is flying. So, the domain would be all the time values \( t \geq 0 \), because we can’t go back in time for this scenario.
In short, \( (f+g)(t) \) helps us understand how high the rocket is above the ground, taking into account the height of the platform, as time goes on starting from when the rocket is launched!