The graph is an illustration of the distance time graphs, and the graph direction changes at different intervals
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:
See attachment for graph
This represents the x values where the height of the balloon experiences an increment.
From the graph (see attachment), the height increases from x = 0 to x = 2
Hence, the interval of the domain where the water balloon's height is increasing is [0,2]
This represents the x values where the height of the balloon remains unchanged
From the graph, the height remains unchanged from x = 2 to x = 4
Hence, the interval of the domain where the water balloon's height stays the same is [2,4]
From the graph, the height decreases by 38 feet from x = 4 to x = 6 and the height decreases by 40 feet from x = 6 to x = 10
The rate of change at these points is:
Point 1 = (38)/(6 - 4) = 19
Point 2 = (40)/(10 - 6) = 10
19 is greater than 10;
This means that the height decreases fastest at x = 4 to x = 6
Hence, the interval of the domain where the water balloon's height decrease fastest is [4,6]
This means that we determine the value of the graph, when x = 10
From the graph;
y = 0, when x = 10
Hence, the height of the water balloon at 10 seconds is 0 feet
Read more about distance time graphs at:
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