The domain of the function is 0 ≤ t ≤ 10. Therefore, 0 ≤ t ≤ 10 is correct.
In the context of a function representing the motion of a thrown ball, the domain is a crucial concept defining the set of all possible input values for the function.
In this case, the input variable is time, denoted by t, measured in seconds.
The graph of the function visually illustrates the behavior of the ball over a specific time interval.
The depicted scenario involves the ball being thrown at t=0 and landing at t=10.
Consequently, the domain of the function is determined by the valid time values during this event.
The inclusive inequality 0≤t≤10 signifies that the function is defined and meaningful for any time value within the range of 0 seconds to 10 seconds.
This domain restriction is grounded in the practical constraints of the physical situation being modeled—specifically, the time interval during which the ball is in motion.
The domain is essential for interpreting and analyzing the function accurately.
It ensures that the function is only evaluated for time values that are relevant to the motion of the ball, preventing the application of the function beyond the defined temporal boundaries of the scenario.