1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $-3 \leq x \leq 3$. 2. **Recall the formula:** The average rate of change of a function $f(x)$ over an interval $[a,b]$ is given by $$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$$ This formula calculates the slope of the secant line connecting the points $(a, f(a))$ and $(b, f(b))$ on the graph. 3. **Identify the points:** From the problem, we have $$a = -3, \quad f(a) \approx -60$$ $$b = 3, \quad f(b) \approx 60$$ 4. **Apply the formula:** $$\frac{f(3) - f(-3)}{3 - (-3)} = \frac{60 - (-60)}{3 + 3} = \frac{60 + 60}{6} = \frac{120}{6}$$ 5. **Simplify the fraction:** $$\frac{\cancel{120}}{\cancel{6}} = 20$$ 6. **Interpretation:** The average rate of change of $f(x)$ on the interval $[-3,3]$ is $20$. This means that on average, the function increases by 20 units in $y$ for every 1 unit increase in $x$ over this interval. **Final answer:** $$\boxed{20}$$