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, 80 and 3, 80 and 4, 20 and 6, 0 and 7, 0 and 8, 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 10 seconds. use complete sentences to support your answer. (3 points)

Part A) Interval [0,2]

Part B) Interval [2,3]

Part C) In the interval [3,4] the water balloon's height decreasing the fastest

Part D) The water balloon's height at 10 seconds is equal to zero

Step-by-step explanation:

Part A: During what interval(s) of the domain is the water balloon's height increasing?

see the attached figure to better understand the problem

During the interval [0,2] the height of the water balloon is increasing

All real numbers greater than or equal to 0 seconds and less than or equal to 2 seconds

The slope of the linear equation in that interval is positive

Part B: During what interval(s) of the domain is the water balloon's height staying the same?

Looking at the graph

During the interval [2,3]  the water balloon's height is the same

All real numbers greater than or equal to 2 seconds and less than or equal to 3 seconds

The slope of the linear equation in that interval is equal to zero ( is a horizontal line)

Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest?

Determine the slope

The formula to calculate the slope between two points is equal to

Interval [3,4]

For x= 3 sec > h=80 ft

For x= 4 sec > h=20 ft

substitute

Interval [4,6]

For x= 4 sec > h=20 ft

For x= 6 sec > h=0 ft

substitute

therefore

In the interval [3,4] the water balloon's height decreasing the fastest, because the graph has the steepest negative slope

Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 10 seconds

Looking at the graph

we know that

For > the water balloon's height  is equal to zero

therefore

The water balloon's height at 10 seconds is equal to zero

1/800 is the right answer