Question

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

Answer 1

Answer:

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

Step-by-step 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$=\frac{f(b)-f(a)}{b-a}$

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

$=\frac{f(b)-f(a)}{b-a}\\\\=\frac{4-1}{4-3}=\frac{3}{1}=3$

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