# Average Rate of Change Formula

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

### Formula for the Average Rate of Change of a Function

Using function notation, we can define the Average rate of Change of a function f from a to x as

Where,
f(a) and f(x) are the value of the function f(x) at the range ‘a’ and ‘b’ and ‘a’ and ‘b’ are the range limit.

### Solved Examples

Question 1: Calculate the average rate of change of a function, f(x) = 3x + 12 as x changes from 5 to 8 ?

Solution:Given,
f(x) = 3x + 12
a = 5
b = 8f(5) = 3(5) + 12
f(5) = 15 + 12
f(5) = 27f(8) = 3(8) + 12
f(8) = 24 + 12
f(8) = 36The average rate of change is,
A(x) = $\frac{f(b)-f(a)}{b-a}$A(x) = $\frac{f(8)-f(5)}{8-5}$

A(x) = $\frac{36-27}{3}$

A(x) = $\frac{9}{3}$

A(x) = 3