1 Answer

KingJackaL · Answer 1 · 2023-05-20T18:59:43+0000

Average rate of change of a function

Initial explanation

We know that the average rate of change of a function between the point

x = a

and the point

x = b

is given by the formula:

$(f(b)-f(a))/(b-a)=(\Delta y)/(\Delta x)$

This is how much the function changed on the y axis divided by the change in the x axis.

In this case, we have that the points a and b are x = 2 and x = 4:

We can observe that

when x = 2

then f(2) = -3

when x = 4

then f(4) = -15

Then, using the formula, we have:

$\begin{gathered} (f(b)-f(a))/(b-a)=(\Delta y)/(\Delta x) \\ \downarrow \\ (f(4)-f(2))/(4-2)=(-15-(-3))/(2) \\ =(-12)/(2)=-6 \end{gathered}$