Question

What does average rate of change mean?

Answer 1

The average rate of change of a function `y=f(x)`, 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 `x1` to `x2` the value of the function changes from `y1` to `y2`. The average rate of change will be:
`(y2-y1)/(x2-x1)` and it is, basically the slope of the blue line.

For example:
if `x1=1` and `x2=5`
and:
`y1=2` and `y2=10`
you get that:
Average rate of change`=(10-2)/(5-1)=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.