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

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
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 $g(x)=\frac{5}{x - 1}+2$.
$$
\begin{align*}
g(-4)&=\frac{5}{-4-1}+2\
&=\frac{5}{-5}+2\
&=-1 + 2\
&=1
\end{align*}
$$
## Step3: Calculate $g(3)$
Substitute $x = 3$ into $g(x)=\frac{5}{x - 1}+2$.
$$
\begin{align*}
g(3)&=\frac{5}{3-1}+2\
&=\frac{5}{2}+2\
&=\frac{5 + 4}{2}\
&=\frac{9}{2}
\end{align*}
$$
## Step4: Calculate the average rate of change
Use the formula $\frac{g(b)-g(a)}{b - a}$, with $a=-4$, $b = 3$, $g(-4)=1$, and $g(3)=\frac{9}{2}$.
$$
\begin{align*}
\frac{g(3)-g(-4)}{3-(-4)}&=\frac{\frac{9}{2}-1}{3 + 4}\
&=\frac{\frac{9-2}{2}}{7}\
&=\frac{\frac{7}{2}}{7}\
&=\frac{1}{2}
\end{align*}
$$

# Answer:
A. $\frac{1}{2}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(g(-4)\)

Step3: Calculate \(g(3)\)

Step4: Calculate the average rate of change

Answer: