Will mark ! analyze the function f(x) = sec 2x. include: - domain and range - period and amplitude - two vertical asymptotes

Given trigonometric function is f(x)=

Therefore domain of f(x) is all the real numbers which make f(x) defined

Here f(x) is not defined at cos 2x=0

⇒f(x) is not defined at 2x=⇒ [as ]

Therefore domain of f(x)={x∈|x≠,where n is an integer}

and the vertical asymptotes are those where f(x) is not defined

i.e. the vertical asymptotes are,where n is an

integer.

By substituting value of x=0,1  two asymptotes are

,

Range is the union of two infinite intervals: y≤-1 and y≥1.

or Range=(-∞, -1] U [ 1, ∞)

There is no horizontal asymptotes .

The period=

The graph of sex 2x has no maximum or minimum value ∴There is  no amplitude.

5050

hope this !