Suppose the function, g(x), 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(x)?

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 .

the ball reaches its maximum height of 15 feet in 2.2 seconds .

The ball takes 2.2 seconds to reach the maximum height from the ground

Ball takes another 2.2 seconds to reach the ground from the maximum height

So 2.2+ 2.2 = 4.4 seconds

The ball will be in the air for 4.4 seconds

So the domain of g(x) is 0 to 4.4 seconds

[0,4.4] is the domain in interval form

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).