uppose the function, g left-parenthesis x right-parenthesis, is used to model the height, y, of a soccer ball, x seconds after the ball is kicked up in the air. The ball starts on the ground and travels in a parabolic shape as it reaches a maximum height and then returns to the ground. Suppose further that the ball reaches its maximum height of 15 feet in 2.2 seconds. What would be an appropriate domain for g left-parenthesis x right-parenthesis?
(1 point)
Responses
0 less-than-or-equal-to x less-than-or-equal-to
Image with alt text: 0 less-than-or-equal-to x less-than-or-equal-to
negative 2.2 less-than-or-equal-to x less-than-or-equal-to 2.2
Image with alt text: negative 2.2 less-than-or-equal-to x less-than-or-equal-to 2.2
0 less-than-or-equal-to x less-than-or-equal-to 4.4
Image with alt text: 0 less-than-or-equal-to x less-than-or-equal-to 4.4
0 less-than-or-equal-to x less-than-or-equal-to 15
The appropriate domain for g(x) would be 0 ≤ x ≤ 4.4.
The appropriate domain for g(x) would be 0 less-than-or-equal-to x less-than-or-equal-to 4.4.
To determine an appropriate domain for the function g(x), which models the height of the soccer ball, we need to consider the given information.
It is mentioned that the ball reaches its maximum height of 15 feet in 2.2 seconds.
Since the ball starts on the ground and travels in a parabolic shape, it means that the ball will reach the ground again at some point.
Therefore, the ball's height is only meaningful within the time frame starting from when it is kicked up until it touches the ground again.
To find the appropriate domain, we need to consider the time it takes for the ball to reach the top of its trajectory (maximum height) and the time it takes for the ball to reach the ground again.
In this case, the ball takes 2.2 seconds to reach its maximum height and it will take an equal amount of time to return to the ground.
So, the total time it stays in the air is 2.2 seconds + 2.2 seconds = 4.4 seconds.
Therefore, an appropriate domain for g(x) would be:
0 ≤ x ≤ 4.4
This means that the function g(x) is defined for values of x from 0 to 4.4 seconds inclusive.