Average rate of change f(x)

Question

Maciej Morrow · Accepted Answer

It is defined as the ratio of the difference in the function f(x) as it changes from

x_{1}

to

x_{2}

and the difference between

x_{1}

and

x_{2}

.
Given:

f (x) = - 3 x + 8

and change in x value from -2 to 3
Formula used: Average rate of change

= \frac{f (x_{2}) - f (x_{1})}{x_{2} - x_{1}}

Calculation:
Step 1: Identify

x_{1}

and

x_{2}

Since the x value changed from -2 to 3; so

x_{1} = - 2

and

x_{2} = 3

Step 2: Calculate

f (x_{1})

and

f (x_{2})

f (- 2) = - 3 (- 2) + 8 = 6 + 8 = 14

f (3) = - 3 (3) + 8 = - 9 + 8 = - 1

Step 3: Plug the formula

\frac{f (x_{2}) - f (x_{1})}{x_{2} - x_{1}}

\frac{- 1 - 14}{3 - (- 2)} = \frac{- 15}{3 + 2} = - \frac{15}{5} = - 3

Alternative approach: For a linear function, the average rate of change is equal to the slope. If we pattern match our function with

y = m x + b

, the slope (value of m) for given function is -3 hence average rate of change is -3.

Answered question