Question

Please help me :)) im struggling.

Answer 1

`= -(1)/(3)`

Explanation:

Given:

`f(x) = (4x - 6)/(x)`

Required:

Average range of change over [-3, 6]

SOLUTION:

Find f(-3) and f(6):

To find f(-3), replace x with -3 in the given function

`f(-3) = (4(-3) - 6)/(-3)`

`f(-3) = (-12 - 6)/(-3)`

`f(-3) = (-18)/(-3)`

`f(-3) = 6`

To find f(6), replace x with 6 in the given function

`f(6) = (4(6) - 6)/(6)`

`f(6) = (24 - 6)/(6)`

`f(6) = (18)/(6)`

`f(6) = 3`

Average rate of change =
`(f(b) - f(a))/(b - a)`

Where,

`a = -3, f(a) = 6`

`b = 6, f(b) = 3`

Plug in the values into the formula for average rate of change.

`= (3 - 6)/(6 -(-3))`

`= (-3)/(9)`

`= (-1)/(3)`

Average rate of change
`= -(1)/(3)`