select the correct answer. consider function ...
select the correct answer. consider function g. g(x)=5/(x - 1)+2 what is the average rate of change of function g over the interval -4, 3? a. -1/2 b. 2 c. 1/2 d. -7/2
Answer
# 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. $\frac{1}{2}$