1. **Problem statement:** Sketch the function $f(x) = \cot(x)$ and mark its points of discontinuity. 2. **Formula and definition:** The cotangent function is defined as $\cot(x) = \frac{\cos(x)}{\sin(x)}$. 3. **Important rules:** - $\cot(x)$ is undefined where $\sin(x) = 0$ because division by zero is undefined. - The sine function is zero at $x = k\pi$ for all integers $k$. 4. **Points of discontinuity:** - Therefore, $f(x)$ has vertical asymptotes (discontinuities) at $x = k\pi$, where $k$ is any integer. 5. **Behavior between discontinuities:** - Between these points, $\cot(x)$ is continuous and decreases from $+\infty$ to $-\infty$. 6. **Summary:** - The graph of $f(x) = \cot(x)$ has vertical asymptotes at $x = k\pi$. - It is periodic with period $\pi$. Final answer: The function $f(x) = \cot(x)$ is discontinuous at $x = k\pi$ for all integers $k$ and continuous elsewhere.