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:
[tex]\frac{f(b)-f(a)}{b-a}=\frac{\Delta y}{\Delta x}[/tex]
This is how much the function changed on the y axis divided by the change in the x axis.
For this quadratic function...
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:
[tex]\begin{gathered} \frac{f(b)-f(a)}{b-a}=\frac{\Delta y}{\Delta x} \\ \downarrow \\ \frac{f(4)-f(2)}{4-2}=\frac{-15-(-3)}{2} \\ =\frac{-12}{2}=-6 \end{gathered}[/tex]
Answer: C. -6
