Question

Using the graph below, calculate the average rate of change for f(x) from x = 0 to x = 2.

Answer 1

we know that

Using the graph

For $x=0$ -----> $f(0)=-2$

For $x=2$ -----> $f(2)=6$

the average rate of change is equal to

$\frac{f(2)-f(0)}{2-0} =\frac{6-(-2)}{2}=4$

therefore

the answer is

the average rate of change is $4$

Answer 2

$A(x) = \frac{f(x) - f(a)}{x - a}$
$A(x) = \frac{f(2) - f(0)}{2 - 0}$
$A(x) = \frac{6 - (-2)}{2}$
$A(x) = \frac{6 + 2}{2}$
$A(x) = \frac{8}{2}$
$A(x) = 4$