Question

(07.06 MC) The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.

Answer 1

2.

Explanation:

We have been given the formula of a function
`f(x)=2x+1`. We are asked to find the average rate of change of the given function between
`x=0` and
`x=3`.

To find the average rate of change we will use formula:

`\text{Average rate of change}=(f(b)-f(a))/(b-a)`

Upon substituting our given values in above formula we will get,

`\text{Average rate of change}=(f(3)-f(0))/(3-0)`

`\text{Average rate of change}=(2\cdot 3+1-(2\cdot 0+1))/(3-0)`

`\text{Average rate of change}=(6+1-(0+1))/(3)`

`\text{Average rate of change}=(6)/(3)`

`\text{Average rate of change}=2`

Therefore, the average rate of change for our given function between
`x=0` and
`x=3` is 2.

Answer 2

Find the rate of change at x=0 and at x=3, then find the average of those values.

f(0) = 2(0) + 1 = 1
f(3) - 2(3) + 1 = 7


`(f(0)+f(3))/(2) = (1 + 7)/(2) = (8)/(2) = 4`

Answer: 4