Question

How does h(x) = 3x - 8 change over the interval from x =3 to x=4

Answer 1

The average rate of change of the function
`h(x) = 3x - 8` over the interval
`x =3\ to\ x=4` is
`3`

Explanation:

Given function is
`h(x) = 3x - 8`

Let
`f(x) = 3x - 8`

And the interval is
`x =3\ to\ x=4`

The average rate of change of the function over the interval to is given by

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

Plug the value in the equation we get,

`a=3\\f(3)=3(3)-8\\=9-8\\f(3)=1\\\\b=4\\f(4)=3(4)-8\\=12-8\\f(4)=4`

The average rate of change

`=(f(b)-f(a))/(b-a)\\\\=(4-1)/(4-3)=(3)/(1)=3`

So, the average rate of change of the function
`h(x) = 3x - 8` over the interval
`x =3\ to\ x=4` is
`3`