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 \( g(x) \) from \( x = 0 \) to \( x = 6 \), we use the formula for the average rate of change:

\[
\text{Average rate of change} = \frac{g(x_2) - g(x_1)}{x_2 - x_1}
\]

Given:
- \( x_1 = 0 \), \( g(0) = 2 \)
- \( x_2 = 6 \), \( g(6) = 4 \)

Now, substitute the values into the formula:

\[
\text{Average rate of change} = \frac{g(6) - g(0)}{6 - 0} = \frac{4 - 2}{6} = \frac{2}{6} = \frac{1}{3}
\]

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

Would you like further details or clarifications?

Here are 5 related questions for deeper exploration:
1. What is the rate of change of \( g(x) \) from \( x = 2 \) to \( x = 8 \)?
2. How would you interpret a negative average rate of change?
3. How does the rate of change affect the shape of the graph of \( g(x) \)?
4. What is the average rate of change of \( f(x) \) from \( x = 0 \) to \( x = 9 \)?
5. How can you find the instantaneous rate of change of \( g(x) \) at \( x = 4 \)?

**Tip:** The average rate of change between two points can be thought of as the slope of the line connecting those points on a graph.

Given the tables for & below, find the following: Average rate of change of g from x = 0 to x = 6 is

Learn how to find the average rate of change of g(x) from x = 0 to x = 6 using the formula (g(x2) - g(x1)) / (x2 - x1). This problem covers key concepts in algebra and functions, and is suitable for students in Grades 9-12.

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