find the average rate of change of $g(x)=\frac{1}{x}$ over the interval $-3,5$. 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, $a=-3$, $b = 5$, and $g(x)=\frac{1}{x}$.

Step2: Calculate $g(a)$ and $g(b)$

$g(-3)=\frac{1}{-3}=-\frac{1}{3}$ and $g(5)=\frac{1}{5}$.

Step3: Substitute into the formula

$\frac{g(5)-g(-3)}{5-(-3)}=\frac{\frac{1}{5}-\left(-\frac{1}{3}\right)}{5 + 3}=\frac{\frac{1}{5}+\frac{1}{3}}{8}$.

Step4: Find a common denominator for the numerator

$\frac{1}{5}+\frac{1}{3}=\frac{3+5}{15}=\frac{8}{15}$.

Step5: Divide by 8

$\frac{\frac{8}{15}}{8}=\frac{8}{15}\times\frac{1}{8}=\frac{1}{15}\approx0.1$.

Answer:

$\frac{1}{15}$ (or approximately $0.1$)