Answer to Question #151442 in Calculus for John Balton

Question

Analyze the function f(x) = - 2 cot 3x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes

Answer 1

$domain\ :\ x \ne \dfrac{\pi}{6} + \dfrac{\pi n}{3} , \ n \in N\\ range \ :\ y \in R\\ period\ : \ \dfrac{\pi}{|b|} = \dfrac{\pi}{|3|} = \dfrac{\pi}{3}\\ vertical\ asymptotes\ : x = \dfrac{\pi}{6} + \dfrac{\pi n}{3}, \ n \in N\\$