3. X | 1 | 2 | 3 | 4 | 5 | 6f(x) | -3 | -1 | 1 | 2 | 5 | 10Selected values of a function f are shown in the table above. What is the average rate of change of f over the interval [1, 6]?A. (6-1)/[10-(-3)]B. [10 + (-3)]/(6+1)C. [10-(-3)]/(6-1)D. [(-3) + (-1) + 1 + 2 + 5 + 10]/6
The average rate of change of a function over an interval is calculated by finding the difference in function values divided by the difference in input values
The average rate of change of a function over an interval is calculated by finding the difference in function values divided by the difference in input values.
In this case, we want to find the average rate of change of f over the interval [1, 6].
To do so, we subtract the initial value of f from the final value of f and divide it by the difference in the input values.
The initial value of f at x=1 is -3, and the final value of f at x=6 is 10. The difference in the input values is 6 – 1 = 5.
Therefore, the average rate of change of f over the interval [1, 6] is (10 – (-3))/5.
Simplifying the expression, we have (10 + 3)/5.
Therefore, the answer is (10 + 3)/5, which is equal to 13/5.
So, the correct answer is not listed among the options provided.
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