# What does average rate of change mean?

Jul 31, 2015

The average rate of change of a function $y = f \left(x\right)$, for example, tells you of how much the value of the function changes when $x$ changes.

#### Explanation:

Consider the following diagram:

when $x$ changes from $x 1$ to $x 2$ the value of the function changes from $y 1$ to $y 2$. The average rate of change will be:
$\frac{y 2 - y 1}{x 2 - x 1}$ and it is, basically the slope of the blue line.

For example:
if $x 1 = 1$ and $x 2 = 5$
and:
$y 1 = 2$ and $y 2 = 10$
you get that:
Average rate of change$= \frac{10 - 2}{5 - 1} = \frac{8}{4} = 2$

This means that for your function: color(red)("every time "x" increases of 1 then "y" increases of 2"
Obviously your function is not a perfect straight line and it will change differently inside that interval but the average rate can only evaluate the change between the two given points not at each individual point.