Question

Based on the graph above, estimate (to one decimal place) the averagerate of change from x = 1 to x= 3

Answer 1

The Average Rate of Change of a function from x=a to x=b is given as:

$A=\frac{f(b)-f(a)}{b-a}$

Substitute a=1 and b=3 into the formula:

$A=\frac{f(3)-f(1)}{3-1}$

Notice from the graph that the value of the function at x=1 is about 2.8, therefore f(1)=2.8. Notice also that the value of the function is 2 at x=3, so f(3)=2.

Substitute these values into the equation:

$A=\frac{2-2.8}{3-1}=\frac{-0.8}{2}=-0.4$

The average rate of change is about -0.4.