Answer: The correct option is (B) [tex]\dfrac{1}{2}.[/tex]
Step-by-step explanation: We are given to find the rate of change between f(-4) and f(0) from the following table:
x -4 -2 0 2 4
f(x) -2 -1 0 1 2
The average rate of change of a function f(x) from x = a to x = b is given by
[tex]A=\dfrac{f(b)-f(a)}{b-a}.[/tex]
From the given table, we have
f(-4) = - 2 and f(0) = 0.
Therefore, the average rate of change between f(-4) and f(0) is given by
[tex]A=\dfrac{f(0)-f(-4)}{0-(-4)}=\dfrac{0-(-2)}{0+4}=\dfrac{2}{4}=\dfrac{1}{2}.[/tex]
Thus, the required rate of change is [tex]\dfrac{1}{2}.[/tex]
Option (B) is correct.
