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

Explanation:

Step1: Calculate $f(x_1)$

Substitute $x_1=-6$ into $f(x)=\sqrt{-7x - 1}$. $f(-6)=\sqrt{-7\times(-6)-1}=\sqrt{42 - 1}=\sqrt{41}\approx6.403$

Step2: Calculate $f(x_2)$

Substitute $x_2 = - 2$ into $f(x)=\sqrt{-7x - 1}$. $f(-2)=\sqrt{-7\times(-2)-1}=\sqrt{14 - 1}=\sqrt{13}\approx3.606$

Step3: Use average - rate - of - change formula

The average rate of change formula is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x_1=-6$, $x_2=-2$, $f(x_1)\approx6.403$, $f(x_2)\approx3.606$. $\frac{f(-2)-f(-6)}{-2-(-6)}=\frac{3.606 - 6.403}{-2 + 6}=\frac{-2.797}{4}=-0.70$

Answer:

$-0.70$