question 2 of 13, step 1 of 1 what is the average rate of change of f(x) from x1 = -4 to x2 = -3? please…

Explanation:

Step1: Calculate $f(x_1)$

Substitute $x_1=-4$ into $f(x)=\sqrt{-8x - 2}$. $f(-4)=\sqrt{-8\times(-4)-2}=\sqrt{32 - 2}=\sqrt{30}\approx5.48$

Step2: Calculate $f(x_2)$

Substitute $x_2=-3$ into $f(x)=\sqrt{-8x - 2}$. $f(-3)=\sqrt{-8\times(-3)-2}=\sqrt{24 - 2}=\sqrt{22}\approx4.69$

Step3: Calculate average rate of change

The formula for average rate of change of $y = f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. $\frac{f(-3)-f(-4)}{-3-(-4)}=\frac{\sqrt{22}-\sqrt{30}}{-3 + 4}=\sqrt{22}-\sqrt{30}\approx4.69 - 5.48=-0.79$

Answer:

$-0.79$