Question

What is the average rate of change between:

X=1 and x=2? ___
X=2 and x=3? ___
X=3 and x=4? ___

Answer 1

X=1 and x=2? 2

X=2 and x=3? 4

X=3 and x=4? 8

For this function, the average rate of change increases as x increases.

Answer 2

1. 2

2. 4

3. 8

Explanation:

The average rate of change can be calculated using formula:

`(f(x_2)-f(x_1))/(x_2-x_1)`

1. When
`x_1=1,\ x_2=2,` then the average rate of change is

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

2. When
`x_1=2,\ x_2=3,` then the average rate of change is

`(f(3)-f(2))/(3-2)=(8-4)/(1)=4`

3. When
`x_1=3,\ x_2=4,` then the average rate of change is

`(f(4)-f(3))/(4-3)=(16-8)/(1)=8`