Question

calculate the rate of change of the function on the interval 1, 3.
g(x)=log₃(x)
1/2
-2
2
1

Explanation:

Step1: Recall rate - of - change formula

The average rate of change of a function $y = g(x)$ on the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a = 1$, $b = 3$, and $g(x)=\log_3(x)$.

Step2: Calculate $g(3)$ and $g(1)$

$g(3)=\log_3(3)=1$ since $3^1 = 3$, and $g(1)=\log_3(1)=0$ since $3^0 = 1$.

Step3: Apply the formula

The average rate of change is $\frac{g(3)-g(1)}{3 - 1}=\frac{1 - 0}{2}=\frac{1}{2}$.

Answer:

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