To find the average rate of change of a function $g(x)$ from $x = a$ to $x = b$, we use the formula:

$\text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a}$

In your case, $a = 0$ and $b = 6$. Using the table, we have:

• $g(0) = 2$
• $g(6) = 4$

Now, substitute these values into the formula:

$\text{Average Rate of Change} = \frac{g(6) - g(0)}{6 - 0} = \frac{4 - 2}{6} = \frac{2}{6} = \frac{1}{3}$

So, the average rate of change of $g$ from $x = 0$ to $x = 6$ is $\frac{1}{3}$.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the average rate of change of $g(x)$ from $x = 2$ to $x = 9$?
2. How does the average rate of change differ from the instantaneous rate of change?
3. Can you explain why the average rate of change formula resembles the slope formula?
4. How would you interpret the average rate of change if it was negative?
5. What is the significance of knowing the average rate of change in real-world problems?

Tip: The average rate of change gives the overall trend of a function over an interval, much like the slope between two points on a graph.