Question

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

x -4 -2 0 2 4
f(x) -2 -1 0 1 2

A.2
B.1/2
C.-1/2
D.-2

Answer 1

Answer: The correct option is (B)
`(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=(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=(f(0)-f(-4))/(0-(-4))=(0-(-2))/(0+4)=(2)/(4)=(1)/(2).`

Thus, the required rate of change is
`(1)/(2).`

Option (B) is correct.