1. **State the problem:** Find the domain of the function $$f(x) = \frac{x}{x^2 - 36}$$ using interval notation. 2. **Recall the domain rule:** The domain of a function includes all real numbers except where the denominator is zero because division by zero is undefined. 3. **Set the denominator equal to zero to find restrictions:** $$x^2 - 36 = 0$$ 4. **Solve for x:** $$x^2 = 36$$ $$x = \pm 6$$ 5. **Exclude these values from the domain:** The function is undefined at $$x = -6$$ and $$x = 6$$. 6. **Write the domain in interval notation:** $$(-\infty, -6) \cup (-6, 6) \cup (6, \infty)$$ 7. **Interpretation:** The function is defined for all real numbers except $$-6$$ and $$6$$, matching the vertical asymptotes seen in the graph. **Final answer:** The domain is $$(-\infty, -6) \cup (-6, 6) \cup (6, \infty)$$.