Question

22

g(x) =
*+
+7
What is the average rate of change of g over the interval —2, 4):

Answer 1

`Rate = 1`

Explanation:

Given

`g(x) = x + 7`

Interval: (-2,4)

Required

Determine the average rate of change

This is calculated using:

`Rate = (g(b) - g(a))/(b-a)`

Where:

`(a,b) = (-2,4)`

So, we have:

`Rate = (g(4) - g(-2))/(4-(-2))`

`Rate = (g(4) - g(-2))/(4+2)`

`Rate = (g(4) - g(-2))/(6)`

Calculate g(4) and g(-2)

`g(4) = 4 + 7 = 11`

`g(-2) = -2 + 7 = 5`

So:

`Rate = (11 - 5)/(6)`

`Rate = (6)/(6)`

`Rate = 1`

Hence, the average rate of change is 1