Final answer:
The average rate of change of f(x) = 2x - 2 is 2 over the given intervals.
Step-by-step explanation:
To find the average rate of change of a function over a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the length of the interval.
a) For the interval [0, 1], the function values are f(0) = -2 and f(1) = 0. The length of the interval is 1 - 0 = 1. Therefore, the average rate of change is (0 - (-2))/1 = 2/1 = 2.
b) For the interval [-1, 1], the function values are f(-1) = -4 and f(1) = 0. The length of the interval is 1 - (-1) = 2. Therefore, the average rate of change is (0 - (-4))/2 = 4/2 = 2.
c) For the interval [-∞, ∞], the function values at any two points will always be the same (2x - 2). Therefore, the average rate of change is always 2.
d) For the interval [2, 4], the function values are f(2) = 2(2) - 2 = 2 and f(4) = 2(4) - 2 = 6. The length of the interval is 4 - 2 = 2. Therefore, the average rate of change is (6 - 2)/2 = 4/2 = 2.