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Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3, is less than or equal to, x, is less than or equal to, 43≤x≤4.xx f, of, xf(x)22 424233 313144 222255 151566 1010

Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3, is less than or equal to, x, is less than or equal to, 43≤x≤4.xx f, of, xf(x)22 424233 313144 222255 151566 1010

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Solution

The average rate of change of a function over an interval [a, b] is given by the formula:

(f(b) - f(a)) / (b - a)

From the table, we can see that when x = 3, f(x) = 31 and when x = 4, f(x) = 22.

So, substituting these values into the formula, we get:

(22 - 31) / (4 - 3) = -9 / 1 = -9

So, the average rate of change of the function over the interval 3 ≤ x ≤ 4 is -9.

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