Question

How do the functions in the tables compare?

Lab Group A:
Time after Launch (sec) | Height (ft)
0 | 0
2 | 48
5 | 75
8 | 48
10 | 0

Lab Group B:
Time after Launch (sec) | Height (ft)
1 | 6
0 | 0
5 | 100
9 | 36
10 | 0

A. Since the maximums occurred at the same x-value, the rockets followed the same path.
B. Since the x-intercepts are the same for both functions, the rockets followed the same path.
C. The rockets were in the air for the same amount of time, but the rocket for group B went higher in the air.
D. The rockets traveled the same height in the air, but the rocket for group B was in the air for a longer time.

Answer 1

The rockets were in the air for the same amount of time, but the rocket for group B went higher in the air.Therefore the correct answer is C). The rockets were in the air for the same amount of time, but the rocket for group B went higher in the air.

Step-by-step explanation:

The comparison of the functions reveals that both Lab Group A and Lab Group B rockets were in the air for the same total time. This is evident by observing the time after launch for both groups, which extends from 0 seconds to 10 seconds. The x-values (time) at the beginning and end are the same for both groups, indicating an equal duration of flight.

However, the discrepancy in the maximum heights achieved by the rockets is noticeable. Lab Group B's rocket reached a height of 100 feet, while the highest point for Lab Group A's rocket was 75 feet. Therefore, option (C) accurately reflects this observation, stating that the rockets were airborne for the same duration, but the rocket from Group B reached a greater height.

The x-intercepts, mentioned in option (B), are not the same for both functions. The x-intercept represents the time when the height is zero, and in this case, Lab Group A's rocket has an x-intercept at both t=0 and t=10, while Lab Group B's rocket has an x-intercept only at t=10. Thus, option (B) is not an accurate characterization of the relationship between the two functions.Therefore the correct answer is C). The rockets were in the air for the same amount of time, but the rocket for group B went higher in the air.