# How do you use the amplitude and period to graph y = 2cscx - 1?

Jul 30, 2018

See details and graph.

#### Explanation:

Period of csc x is period of its reciprocal sin x = $2 \pi$.

$\csc x \notin \left(- 1 , 1\right)$.

Range:  y = 2 csc x - 1 notin (( -2 - 1, 2 - 1 ) = ( - 3, 1 )

Domain: Exclude asymptotic x.

$x \ne k \pi , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

Graph, depicting all these aspects:
graph{(1/2(y+1)sin x - 1)(y+3)(y-1)(x-pi)(x+pi)(x-2pi)(x+2pi)(x+3pi)(x-3pi)(x-4pi)(x+4pi)(x-5pi)(x+5pi)(x-6pi)(x+6pi)=0[-20 20 -13 7]}