The correct option is A: 8
The average rate of change of the function over the interval from x = 1 to x = 3 is calculated as the difference in the function's output values at these two points divided by the difference in the input values:
average rate of change = (f(3) - f(1)) / (3 - 1)
From the table, we can see that f(1) = 2 and f(3) = 18. Therefore:
average rate of change = (18 - 2) / (3 - 1) = 16 / 2 = 8
Therefore, the average rate of change of the function for the interval from x = 1 to x = 3 is 8. This means that on average, the function increases by 8 units for every 1 unit increase in x over this interval.
Therefore, the correct option is A: 8.
The question probable may be:
Several values of a function are given in the table. What is the average rate of change of this function between x=1 and x=3?