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Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: 
Rate of change of
:
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of:
The average rate of change of the function over the interval [0,2] is 1.5
Rate of change of
:
Here the end points are (0,0) and (2,2)
The average rate of change of the function over the interval [0,2] is 1
Rate of change of
:
Here the end points are (0,-1) and (2,0)
The average rate of change of the function over the interval [0,2] is 0.5
Rate of change of
:
Here the end points are (0,0.5) and (2,2.5)
The average rate of change of the function over the interval [0,2] is 1
We can conclude that the <span>function that has the greatest rate of change over the interval [0, 2] is the function a.</span>
Rate of change of
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of
The average rate of change of the function
Rate of change of
Here the end points are (0,0) and (2,2)
The average rate of change of the function
Rate of change of
Here the end points are (0,-1) and (2,0)
The average rate of change of the function
Rate of change of
Here the end points are (0,0.5) and (2,2.5)
The average rate of change of the function
We can conclude that the <span>function that has the greatest rate of change over the interval [0, 2] is the function a.</span>