Question

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

Answer 1

See details and graph.

Explanation:

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

`csc x notin ( - 1, 1 )`.

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

Domain: Exclude asymptotic x.

`x ne k pi, k = 0, +-1, +-2, +-3, ...`

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]}