Suppose 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
The appropriate domain for g(x) would be:
0 ≤ x ≤ 4.4
This is because the ball is kicked up in the air for a certain amount of time (x seconds) before it reaches its maximum height and returns to the ground. Since the maximum height is reached in 2.2 seconds, the ball will be in the air for a total of 2.2 seconds + 2.2 seconds = 4.4 seconds. Thus, the domain of g(x) should include the range of time during which the ball is in the air, which is 0 to 4.4 seconds.
The appropriate domain for g(x) would be 0 ≤ x ≤ 4.4.
To find an appropriate domain for the function g(x), we need to consider the context of the problem and the information given.
In this problem, the function g(x) models the height of a soccer ball x seconds after it is kicked. The ball reaches its maximum height of 15 feet in 2.2 seconds.
Since we are dealing with the height of the ball after it is kicked, it makes sense for the domain of the function to start from 0 (when the ball is kicked) and end when the ball reaches its maximum height (2.2 seconds).
Therefore, an appropriate domain for g(x) would be 0 ≤ x ≤ 2.2.
This means that the input (x) should be greater than or equal to 0 seconds and less than or equal to 2.2 seconds in order to have a meaningful height value for the soccer ball.