find the average rate of change of g(x) = -11 / (x - 8) over the interval -7,-4. write your answer as an…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-7$, $b = - 4$, and $g(x)=\frac{-11}{x - 8}$.

Step2: Calculate $g(-4)$

Substitute $x=-4$ into $g(x)$: $g(-4)=\frac{-11}{-4 - 8}=\frac{-11}{-12}=\frac{11}{12}$

Step3: Calculate $g(-7)$

Substitute $x = - 7$ into $g(x)$: $g(-7)=\frac{-11}{-7 - 8}=\frac{-11}{-15}=\frac{11}{15}$

Step4: Calculate the average rate of change

$\frac{g(-4)-g(-7)}{-4-(-7)}=\frac{\frac{11}{12}-\frac{11}{15}}{3}$ First, find a common denominator for $\frac{11}{12}$ and $\frac{11}{15}$. The common denominator of 12 and 15 is 60. $\frac{11}{12}-\frac{11}{15}=\frac{11\times5}{12\times5}-\frac{11\times4}{15\times4}=\frac{55}{60}-\frac{44}{60}=\frac{55 - 44}{60}=\frac{11}{60}$ Then, $\frac{\frac{11}{60}}{3}=\frac{11}{60}\times\frac{1}{3}=\frac{11}{180}\approx0.1$

Answer:

$\frac{11}{180}\approx0.1$