question 5 of 13, step 1 of 1 what is the average rate of change of f(x) from x1 = -2 to x2 = 6? please…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Calculate $f(x_1)$

Given $f(x)=-4x + 9$ and $x_1=-2$, then $f(x_1)=-4\times(-2)+9=8 + 9=17$.

Step3: Calculate $f(x_2)$

Given $x_2 = 6$, then $f(x_2)=-4\times6+9=-24 + 9=-15$.

Step4: Calculate the average rate of change

Substitute into the formula: $\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{-15 - 17}{6-(-2)}=\frac{-32}{8}=-4$.

Answer:

$-4$