Question

average rate of change for f(x)= -9/x from x=-3 to x=-3+h

Answer 1

Average rate of change is simply slope of the line.

Given function f(x) = -9/x

f(-3) = -9/-3 = 3

f(-3+h) = -9/(-3+h)

The slope of the line connecting two points are say (x1,y1) = (-3,3)

(x2,y2) = ((-3+h),(-9/(-3+h))

Slope m = (y2-y1)/(x2-x1)

m = [(-9/(-3+h)-3]/[(-3+h)-(-3)]

m = [(-9-3(-3+h))/(-3+h)]/[-3+h+3]

m = [(-9+9-3h)/(-3+h)]/h

m = -3h/h(-3+h)

m = -3/(-3+h)

Average rate of change = -3/(-3+h)