To calculate the average rate of change of the function $f$ over the interval $[-3, 3]$, we need to use the formula for the average rate of change:

$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$

where $a = -3$, $b = 3$, and $f(x)$ is the value of the function at points $x = -3$ and $x = 3$.

Step 1: Identify $f(-3)$ and $f(3)$

From the graph:

• When $x = -3$, $f(-3) = 3$ (since the graph crosses the point $(-3, 3)$).
• When $x = 3$, $f(3) = 3$ (since the graph crosses the point $(3, 3)$).

Step 2: Apply the formula

Now, plug these values into the formula:

$\text{Average rate of change} = \frac{f(3) - f(-3)}{3 - (-3)} = \frac{3 - 3}{3 + 3} = \frac{0}{6} = 0$

Thus, the average rate of change of $f$ on the interval $[-3, 3]$ is 0.

Answer:

The correct answer is B. 0.

Would you like more details or have any questions? Here are some related questions:

1. What is the interpretation of the average rate of change in terms of the graph of the function?
2. How is the average rate of change different from the instantaneous rate of change?
3. What are some other methods to calculate the rate of change from a graph?
4. How would the average rate of change differ if the function had a curve instead of straight lines?
5. Can the average rate of change be undefined for some types of functions?

Tip: When calculating the average rate of change from a graph, always check the coordinates of the endpoints on the interval carefully to ensure accuracy.