The average rate of change of a function, f(x), over a given interval [a, b] is given by:
Average rate of change =
Given a table of value for the function f(x) for given x values.
Part 1:
The average rate of change of f(x) over the interval [-5, -1] is given by
.
From the given table, f(-1) = 3 and f(-5) = 35.
Thus, we have
Part 2:
The average rate of change of f(x) over the interval [-4, -1] is given by
.
From the given table, f(-1) = 3 and f(-4) = 24.
Thus, we have
Part 3:
The average rate of change of f(x) over the interval [-3, 1] is given by
.
From the given table, f(1) = -1 and f(-3) = 15.
Thus, we have
Part 4:
The average rate of change of f(x) over the interval [-2, 1] is given by
.
From the given table, f(1) = -1 and f(-2) = 8.
Thus, we have