Question

Find the average rate of change for the given function from x = −1 to x = 2.

Graph of f of x equals negative three x plus 2

Answer 1

`the \: average \: rate \: of \: change = (f(x2) - f(x1))/(x2 - x1) \\ (f(2) - f( - 1))/( 2 - - 1) = \\ ( - 3(2) + 2 - ( - 3( - 1) + 2))/(3) = \\ ( - 6 + 2 - 3 - 2)/(3) = ( - 9)/(3) = - 3`

Answer 2

Average rate of change:
`-3`

Explanation:

We are asked to find average rate of change for our given function
`f(x)=-3x+2`.

We will use average rate of change formula to solve our given problem.

`\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(2)-f(-1))/(2-(-1))`

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

`\text{Average rate of change}=((-6+2)-(3+2))/(2+1)`

`\text{Average rate of change}=((-4)-(5))/(3)`

`\text{Average rate of change}=(-4-5)/(3)`

`\text{Average rate of change}=(-9)/(3)`

`\text{Average rate of change}=-3`

Therefore, the average rate of change for our given function from
`x=-1` to
`x=2` is
`-3`.