The rate of change between x=-2 and x=2 cannot be calculated because y is not defined at x=0 and there is an asymptote at x=0 making the function discontinuous. If y goes from y to h+k when x goes from x to x+h, where h is a small displacement, then k=8/(x+h)-8/x=8(x-(x+h))/(x(x+h)).
Therefore k=-8h/x² because h is small enough to be ignored compared to x.
The rate of change is the slope k/h=-8/x².
When x=-2 or 2, the rate of change is -8/4=-2.
When x=-1 or 1, the rate of change is -8/1=-8.
As x approaches 0, the rate of change increases to negative infinity. For example, x=±0.1, the rate of change is -800.
The rate of change can only be measured provided x≠0.