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, $a=-4$, $b = 3$, and $g(x)=\frac{5}{x - 1}+2$.

Step2: Calculate $g(-4)$

Substitute $x=-4$ into $g(x)$: [ \begin{align*} g(-4)&=\frac{5}{-4 - 1}+2\ &=\frac{5}{-5}+2\ &=-1 + 2\ &=1 \end{align*} ]

Step3: Calculate $g(3)$

Substitute $x = 3$ into $g(x)$: [ \begin{align*} g(3)&=\frac{5}{3-1}+2\ &=\frac{5}{2}+2\ &=\frac{5 + 4}{2}\ &=\frac{9}{2} \end{align*} ]

Step4: Calculate the average rate of change

[ \begin{align*} \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} \end{align*} ]

Answer:

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