Analyze the function f(x) = - 2 cot 3x. include:
- domain and range
- period
- two vertical asymptotes

Answer and Explanation :

Given : Function

To find :

1) Domain and range

2) Period  

3) Two Vertical Asymptotes    

Solution :

1) Domain is defined as the set of possible values of x where function is defined.

For domain,

So,

The value of x is define as

The domain of the function is all real numbers except

The range is defined as all the y values for every x.

So, The range of the function is all real numbers.

2) The general form of the cot function is

Where, Period is

On comparing, B=3

So, The period of the given function is

3) Vertical asymptote is defined as the line which approaches to infinity but never touches the line.

The vertical asymptote is at where function is not defined.

The two vertical asymptote is

Put n=0,

Put n=1,

So, The two vertical asymptote are

7

step-by-step explanation:

squares, rhombus, rectangles