Based on the table below, what is the average rate of change for the interval [-6, 6]?

To calculate the average rate of change for a given interval from a table, we define the average rate of change of a function $f(x)$ over the interval $[a, b]$ using the formula:

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

Given Data

1. Let's assume the values of $f(-6)$ and $f(6)$ can be extracted from the table you have, but since the table is not provided here, I'll demonstrate the steps assuming we have these values.

Steps to Calculate the Average Rate of Change

1. Identify the Interval Points:

   • Let $a = -6$
   • Let $b = 6$

2. Retrieve Function Values:

   • Suppose $f(-6)$ and $f(6)$ are the function values at the points $-6$ and $6$ respectively. Let's denote them as:
     • $f(-6) = y_1$
     • $f(6) = y_2$

3. Apply the Average Rate of Change Formula:

   • Substitute the values into the formula: $\text{Average Rate of Change} = \frac{y_2 - y_1}{6 - (-6)} = \frac{y_2 - y_1}{12}$

4. Perform the Calculation:

   • Compute $y_2 - y_1$.
   • Divide by $12$ to find the average rate of change.

Verify and Summarize

• Ensure that $y_1$ and $y_2$ are correctly retrieved from the table.
• Summarize the findings in terms of numerical values based on the final computation.

Final Answer

Assuming we had the values from the table, the average rate of change over the interval $[-6, 6]$ would be computed as described and presented succinctly. Without the specific values from your table, I am unable to provide a final numerical answer. Please provide the values for $f(-6)$ and $f(6)$ to complete this calculation.