Question

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

Answer 1

Answer:

Average rate of change: $-3$

Step-by-step 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.

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

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

$\text{Average rate of change}=\frac{f(2)-f(-1)}{2-(-1)}$

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

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

$\text{Average rate of change}=\frac{(-4)-(5)}{3}$

$\text{Average rate of change}=\frac{-4-5}{3}$

$\text{Average rate of change}=\frac{-9}{3}$

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

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

Answer 2

$the \: average \: rate \: of \: change = \frac{f(x2) - f(x1)}{x2 - x1} \\ \frac{f(2) - f( - 1)}{ 2 - - 1} = \\ \frac{ - 3(2) + 2 - ( - 3( - 1) + 2)}{3} = \\ \frac{ - 6 + 2 - 3 - 2}{3} = \frac{ - 9}{3} = - 3$