select the correct answer. consider function g. g(x) = 5/(x - 1)+2 what is the average rate of change of…

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, $a=-4$ and $b = 3$.

Step2: Calculate $g(-4)$

Substitute $x=-4$ into $g(x)=\frac{5}{x - 1}+2$: $g(-4)=\frac{5}{-4 - 1}+2=\frac{5}{-5}+2=-1 + 2=1$.

Step3: Calculate $g(3)$

Substitute $x = 3$ into $g(x)=\frac{5}{x - 1}+2$: $g(3)=\frac{5}{3 - 1}+2=\frac{5}{2}+2=\frac{5 + 4}{2}=\frac{9}{2}$.

Step4: Calculate the average rate of change

$\frac{g(3)-g(-4)}{3-(-4)}=\frac{\frac{9}{2}-1}{3 + 4}=\frac{\frac{9 - 2}{2}}{7}=\frac{\frac{7}{2}}{7}=\frac{7}{2}\times\frac{1}{7}=\frac{1}{2}$.

Answer:

C. $\frac{1}{2}$