If the average rate of change of g(x) from x = 1 to x = 9 is 20, and if the average rate of change of g(x) from x = 9 to x = 21 is 40, then what is the average rate of change of g(x) from x = 1 to x = 21?

Answer 1

from 1 to 9, g(x) = 20(x-1)
so, g(9) = g(1) + 160
similarly, g(21) = g(9) + 40(21-9)
= g(9) + 480

So, g(21) = g(1) + 160 + 480 = g(1)+640

640/(21-1) = 640/20 = 32

The average rate of change from x=1 to 21 is 32.

Answer 2

solve using the graphing method y=x-3
y=-1/2x=3