what is the average rate of change of f(x) from x1 = -7 to x2 = -5? please write your answer rounded to the…

Explanation:

Step1: Calculate $f(x_1)$

Substitute $x_1=-7$ into $f(x)=\sqrt{-8x - 5}$. $f(-7)=\sqrt{-8\times(-7)-5}=\sqrt{56 - 5}=\sqrt{51}$

Step2: Calculate $f(x_2)$

Substitute $x_2=-5$ into $f(x)=\sqrt{-8x - 5}$. $f(-5)=\sqrt{-8\times(-5)-5}=\sqrt{40 - 5}=\sqrt{35}$

Step3: Use average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x_1=-7$, $x_2=-5$, $f(x_1)=\sqrt{51}$, $f(x_2)=\sqrt{35}$. So the average rate of change is $\frac{\sqrt{35}-\sqrt{51}}{-5-(-7)}=\frac{\sqrt{35}-\sqrt{51}}{2}$ $\approx\frac{5.916 - 7.141}{2}=\frac{-1.225}{2}=-0.6125\approx - 0.61$

Answer:

$-0.61$