A rocket is launched with an initial velocity of 100 ft/s. The height of the rocket in meters is modeled by the function shown below, where t is time in seconds.

Question

h(t) = -4t² + 120t

Write a statement that describes the 1) domain of this function and 2) range of this function. Make sure to include an explanation as to why you know these values are included in the domain and in the range of the function.

Answer 1

Hello Ariana, The questions about "Domain" and "Range" are asking you to figure out how many seconds are involved with the rocket launch (that is the "Domain") and the different heights the rocket reaches (that is the "Range").

You are told that the height of the rocket "depends" on time (you put a given number of seconds into the function and you get out one height for the rocket).

Questions to ask: can you have negative time? Can the rocket go below ground? If you can answer those questions, you have answered the "Domain" and "Range" part of the problem.

I would encourage you to factor the original version and sketch the function--makes the Domain and Range easy to see. That is, instead of working with:

h(t) = -4t² + 120t

work with the factored form:

h(t) = (-4t)(t - 30)

I hope that you can easily sketch a graph of the factored form, but please let me know if you have questions.