Given the tables for  &  below, find the following:

0	2	8
1	3	5
2	1	4
3	8	0
4	7	6
5	9	9
6	4	2
7	6	3
8	5	1
9	0	7


Average rate of change of g  from x = 0  to x = 6  is   


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.

Given the tables for g(x) below, find the following: 

0  2  8
1  3  5
2  1  4
3  8  0
4  7  6
5  9  9
6  4  2
7  6  3
8  5  1
9  0  7

Average rate of change of g from x = 0 to x = 6 is

Learn how to calculate the average rate of change of the function g(x) from x = 0 to x = 6 using the formula (g(b) - g(a)) / (b - a). This problem covers key concepts in algebra and functions, suitable for students in Grades 9-12.

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