Question

Analyze the function f(x) = - 2 cot 3x. Include:

- Domain and range
- Period
- Two Vertical Asymptotes

Answer 1

For the domain and range, Period, and Two Vertical Asymptotes is stated below

Explanation:

For the function f(x) = - 2 cot 3x.

lets state the following as follows,

y = -2[cos(3x)/sin(3x)]

For the Domain

All Real Numbers except with sin(3x)=0,

All Real Numbers except x = 0 or pi/3

For the Range=All Real Numbers

For the given Period = (2pi/3) = (2/3)pi

For Two Vertical Asymptotes:: x = 0 and x = pi/3

Answer 2

-Domain of the function is :
for all X : X belongs to real numbers. where, 3x > pi x n & 3x < pi (n+1)

- Range of the function is :
All real numbers.

-Period of the function is :
pi/3

- The vertical asymtotes are :
-2 pi/3 and -pi/3