Question

Consider the function f(x)=−5x−8 and find the following: a) The average rate of change between the points (−1,f(−1)) and (3,f(3)) . b) The average rate of change between the points (a,f(a)) and (b,f(b)) . c) The average rate of change between the points (x,f(x)) and (x+h,f(x+h)) .

Answer 1

a. -5

b.-5

c.-5

Explanation:

In order to find the average rate of change of a function , we divide the change in the output value by the change in the input value.

Generally, the average rate of change (ARC) on an ecuatios between two points (x1,f(x1)) and (x2,f(x2)) is

• ARC = [f(x2)-f(x1)]/ (x2-x1)

In case a)

f(-1)= -5*(-1)-8=5-8= -3 f(3)= -5*3-8= -23

Then ARC= (-23-(-3))/(3-(-1))=-20/4=-5

In case b)

f(a)= (-5a-8)

f(b)= (-5b-8)

Then ARC= [(-5b-8)-(-5a-8)]/(b-a)= (-5b+5a)/(b-a)= -5(b-a)/(b-a)= -5

In case c)

f(x)= -5x-8

f(x+h)= -5(x+h)-8= -5x-5h-8

then ARC= [(-5x-5h-8)-(-5x-8)]/(x+h-x) =-5h/h= -5