The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: a linear model with ordered pairs at 0, 60 and 2, 75 and 4, 75 and 6, 40 and 8, 20 and 10, 0 and 12, 0 and 14, 0. the x axis is labeled time in seconds, and the y axis is labeled height in feet. part a: during what interval(s) of the domain is the water balloon's height increasing? (2 points) part b: during what interval(s) of the domain is the water balloon's height staying the same? (2 points) part c: during what interval(s) of the domain is the water balloon's height decreasing the fastest? use complete sentences to support your answer. (3 points) part d: use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds. use complete sentences to support your answer. (3 points)

Part A: 0< x <2

Part B: 2< x <4 and x > 10

Part C: 4 < x < 10

Part D: 0 ft

Step-by-step explanation:

The ordered pairs are (0, 60), (2, 75), (4, 75), (6, 40), (8, 20), (10, 0), (12, 0), (14, 0), where the first number represents the x-axis, the time, and the second the y-axis, the height.

The domain is the set formed by the x values. A  set formed by the y values is the function image.

When x increases and y also increases, the function is crescent, and the height of the balloon is increasing, it happens at the interval 0< x < 2, after 2 seconds, the height remains constant (75 ft) until 4 seconds. After 10 seconds the height remains constant too (0 ft), so the height remains constant at the domain intervals 2 < x < 4 and x > 10.

In the interval 4< x <10, the higher is decreasing (from 75 to 0). After 10 seconds the water balloon has reached the ground (0 ft) so it possible had burst, so, at 16 seconds the higher will remains 0 ft.

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