Question

The table shows the values of a function f(x). What is the average rate of change of f(x) from 1 to 4?

x f(x)
0 500
1 484
2 436
3 356
4 244
5 100

Answer 1

The average rate of change of f(x) from 1 to 4 is -80.

Explanation:

The average rate of change of f(x) from a to b is defined as

`m=(f(b)-f(a))/(b-a)`

The average rate of change of f(x) from 1 to 4 is defined as

`m=(f(4)-f(1))/(4-1)`

`m=(f(4)-f(1))/(3)`

From the given table it is clear that the the value of the function is 244 at x=4 and 484 at x=1. So f(4)=244 and f(1)=484. Put these values in the above equation.

`m=(244-484)/(3)`

`m=(-240)/(3)`

`m=-80`

Therefore the average rate of change of f(x) from 1 to 4 is -80.

Answer 2

-80

Explanation:

The average rate of change is

a.r.c = f(4) - f(1)

--------------

4-1

f(4) = 244 and f(1) = 484

a.r.c = 244 - 484

--------------

3

= -240/3

=-80