Question

Which of the following is the graph of the function y = 4csc(x)

Answer 1

c

Explanation:

Answer 2

C

Explanation:

We are given that a function

`f(x)=4csc(x)`

Domain of function f(x)={x\x
`\\eq n\pi,n\in Z`}

Range of function,f(x)=(
`-\infty,-4]\cup [4,\infty)`

Substitute x=
`(\pi)/(2)`

`f((\pi)/(2))=4csc((\pi)/(2))=4`

`csc((\pi)/(2))=1`

Substitute x=
`-(\pi)/(2)`

`f(-(\pi)/(2))=4csc(-(\pi)/(2))=-4`

`csc(-(\pi)/(2))=-1`

Substitute x=0,
`\pm\pi,\pm 2\pi,`..

`f(0)=\infty=f(\pi)=f(2\pi)=`...

`f(-\pi)=-\infty=f(-2\pi)=`...

Hence, option C is true.