To interpret the function [tex]\( f(t) \)[/tex] correctly, we need to understand the notation [tex]\( f(t) = H \)[/tex]. Here, [tex]\( f(t) \)[/tex] represents the height [tex]\( H \)[/tex] as a function of time [tex]\( t \)[/tex].
Given the statement [tex]\( f(5) = 12 \)[/tex], this means that when [tex]\( t = 5 \)[/tex] seconds, the height [tex]\( H \)[/tex] is 12 meters.
Let's evaluate each option:
1. The object travels 12 meters for every 5 seconds.
- This is incorrect; the given notation does not suggest a continuous travel rate but rather a specific height at a given time.
2. 5 seconds after the object is launched it is 12 meters in the air.
- This is a direct interpretation of [tex]\( f(5) = 12 \)[/tex]. It means that 5 seconds after launch, the height of the object is 12 meters.
3. The object travels 5 meters for every 12 seconds.
- This is also incorrect; it does not align with the interpretation needed for [tex]\( f(5) = 12 \)[/tex].
4. 5 seconds after the object is launched it is traveling 12 meters per second.
- This is incorrect; [tex]\( f(t) \)[/tex] represents height, not velocity.
5. 12 seconds after the object is launched it is 5 meters in the air.
- This is incorrect because it would be represented as [tex]\( f(12) = 5 \)[/tex], which is not related to [tex]\( f(5) = 12 \)[/tex].
6. 12 seconds after the object is launched it is traveling 5 meters per second.
- This is incorrect for the same reason as the previous option; [tex]\( f(t) \)[/tex] represents height, not velocity.
7. The object is 60 meters in the air.
- This is not related to the function [tex]\( f(5) = 12 \)[/tex] and provides no context about time.
Based on the correct interpretation, the best statement is:
5 seconds after the object is launched it is 12 meters in the air.
Thus, the answer is:
The best interpretation of [tex]\( f(5)=12 \)[/tex] is:
5 seconds after the object is launched it is 12 meters in the air.
