Question

✖️-101 2 3 f(✖️) -2-1 -1/2-1/4-1/8 -9/4 -7/12 12/7 7/12 Given the following table,fine the rate of change between f(-1) and f(2).

Answer 1

Answer:
`(7)/(12).`

Explanation:

Given table:

X f(X)

-1 -2

0 -1

1
`-(1)/(2)`

2
`-(1)/(4)`

3
`-(1)/(8)`

i.e. , f(-1) = -2

f(2) =
`-(1)/(4)`

The rate of change between
`f(a)` and
`f(b)=(f(b)-f(a))/(b-a)`

Then, the rate of change between f(-1) and f(2) =
`(-(1)/(4)-(-2))/(2-(-1))`

`=(-(1)/(4)+2)/(3)=((-1+8)/(4))/(3)\\\\=((7)/(4))/(3)\\\\=(7)/(12)`

Hence, the rate of change between f(-1) and f(2) is
`(7)/(12).`