The height of a model rocket, [tex]H(t)[/tex], is a function of the time since it was launched, [tex]t[/tex].

What is the domain of [tex]H(t)[/tex]?



Answer :

To determine the domain of [tex]\( H(t) \)[/tex], we need to consider the context in which the function is defined and any possible constraints on the variable [tex]\( t \)[/tex].

1. Identify the Variable: The variable [tex]\( t \)[/tex] represents the time since the launch of a model rocket. Time is typically measured in non-negative units (seconds, minutes, etc.).

2. Analyze the Meaning: Since [tex]\( t \)[/tex] represents time, it can’t be negative. This means that [tex]\( t \)[/tex] must be a non-negative real number.

3. Define the Domain: The domain of [tex]\( H(t) \)[/tex] will include all possible values of [tex]\( t \)[/tex] for which [tex]\( H(t) \)[/tex] is defined. Since [tex]\( t \)[/tex] is the time elapsed since the launch, and time can start from 0 and extend indefinitely into the future, the domain of [tex]\( t \)[/tex] will be all non-negative real numbers.

Therefore, the domain of [tex]\( H(t) \)[/tex] is given by:
[tex]\[ t \geq 0 \][/tex]

In interval notation, this can be written as:
[tex]\[ [0, \infty) \][/tex]

Hence, the domain of [tex]\( H(t) \)[/tex] is [tex]\((0, \text{inf})\)[/tex].