1. **State the problem:** We need to find the average rate of change of the function over the interval $3 \leq x \leq 7$. 2. **Recall the formula for average rate of change:** $$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$$ where $a$ and $b$ are the endpoints of the interval. 3. **Identify the values from the table:** - $a = 3$, $f(a) = 2$ - $b = 7$, $f(b) = 26$ 4. **Substitute into the formula:** $$\frac{f(7) - f(3)}{7 - 3} = \frac{26 - 2}{7 - 3}$$ 5. **Simplify the numerator and denominator:** $$\frac{24}{4}$$ 6. **Simplify the fraction:** $$\frac{\cancel{24}^{6}}{\cancel{4}^{1}} = 6$$ 7. **Final answer:** The average rate of change of the function over the interval $3 \leq x \leq 7$ is $6$.