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The average rate of change is defined as the change in y-values divided by the change in x-values over the given interval.
So, for the interval [3,4], we have:
Change in y-values: f(4) - f(3) = 24 - 8 = 16
Change in x-values: 4 - 3 = 1
Average rate of change = (Change in y-values)/(Change in x-values) = 16/1 = 16
Therefore, the average rate of change over the interval [3,4] of the given graph of the function is 16.