Question

How do you find the average rate of change of `y=3x-2` over [x,x+h]?

Answer 1

`3`

Explanation:

The average rate of change of the function `f(x)` over the interval `[a,b]` can be expressed as:

`"average rate of change"=(f(b)-f(a))/(b-a)`

So, for the function `f(x)=3x-2` and the interval `[x,x+h]`, this becomes:

`=(f(x+h)-f(x))/((x+h)-x)`

`=((3(x+h)-2)-(3x-2))/h`

`=(3x+3h-2-3x+2)/h`

`=(3h)/h`

`=3`