To find the average rate of change of the function $f(x)$ over the interval $[1, 8]$, we can use the formula for the average rate of change:

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

where $a = 1$ and $b = 8$. Let's use the values from the table:

• $f(1) = -2$
• $f(8) = 3$

Now, substituting these into the formula:

$\text{Average Rate of Change} = \frac{f(8) - f(1)}{8 - 1} = \frac{3 - (-2)}{8 - 1} = \frac{3 + 2}{7} = \frac{5}{7}$

So, the average rate of change of the function $f(x)$ from $x = 1$ to $x = 8$ is $\frac{5}{7}$.

Would you like more details on this, or do you have any other questions?

Here are some related questions you might find interesting:

1. What does the average rate of change tell us about the function between two points?
2. How can the average rate of change be interpreted graphically?
3. How does the average rate of change compare to the instantaneous rate of change?
4. Can the average rate of change be negative? If so, what does that indicate?
5. How would the average rate of change differ if calculated over different intervals?

Tip: The average rate of change is essentially the slope of the secant line between two points on the graph of the function.