Question

12 A bail is placed in a machine that throws the ball up in the air. The table represents some points on the graph of a function that models the ball's distance from the ground with respect to the time since the ball has been thrown.
Ball
Time Since Thrown from Machine (seconds)
0.25 0.50 0.75
1.00
1.25
1.50
1.75
Distance from Ground (meters)
2.76
4.90
6.43
7.35
7.66 7.35
6.43
What is the range for this situation?
0
0
G All real numbers less than or equal to 1.25
F All real numbers less than or equal to 7.66
MA real numbers greater than or equal to oant less than or equal to 7.66
2 Allers greater Than or equal to and less than or ege
Eric

Answer 1

To determine the range for the situation described, we need to identify the lowest and highest values of the distance from the ground at the specified time intervals for the function modeling the ball's height.

From the provided data, the distance from the ground at different time intervals is:

- At 0.25 seconds: 2.76 meters
- At 0.50 seconds: 4.90 meters
- At 0.75 seconds: 6.43 meters
- At 1.00 seconds: 7.35 meters
- At 1.25 seconds: 7.66 meters
- At 1.50 seconds: 7.35 meters
- At 1.75 seconds: 6.43 meters

Now, let's determine the minimum and maximum distances from the ground:

- The minimum distance is **2.76 meters** (at 0.25 seconds).
- The maximum distance is **7.66 meters** (at 1.25 seconds).

Thus, the range of the function modeling the ball's distance from the ground can be expressed as all real numbers greater than or equal to 2.76 and less than or equal to 7.66.

In interval notation, the range is: **[2.76, 7.66]**.

Among the options provided, the best choice that reflects this range is:
- **All real numbers greater than or equal to 2.76 and less than or equal to 7.66.**