Question

Given the following table, find the rate of change between f(-4) and f(0).

Answer 1

Answer:  The correct option is (B) $\dfrac{1}{2}.$

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

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

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

$A=\dfrac{f(0)-f(-4)}{0-(-4)}=\dfrac{0-(-2)}{0+4}=\dfrac{2}{4}=\dfrac{1}{2}.$

Thus, the required rate of change is $\dfrac{1}{2}.$

Option (B) is correct.