How do you graph, identify the domain, range, and asymptotes for $y=1/2cscx-pi-1$ ?

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Answer 1 · 2018-07-28T14:26:35

Range: $y notin ( _ ( pi + 3/2), - ( pi + 1/2 )$
Domain: Asymptotic $x ne k pi, k = 0, +-1,+-2, +-3, ...$

$csc values notin ( - 1, 1 )$ . So,

$y = 1/2 csc x - ( pi + 1 )$

$notin ( - 1/2 - ( pi + 1 ), 1/2 - (pi + 1 ) )$

$= ( - ( pi + 3/2 ), - ( pi + 1/2 ) )$

Domain: Asymptotic $x ne k pi, k = 0, +-1,+-2, +-3, ...$ ,

given by zeros of sin x.

See graph, depicting these aspects.
graph{(2(y+pi+1)sin x-1)(y+pi+1.5)(y+pi+.5)(x^2-(pi)^2)=0[-20 20 -15 5]}

How do you graph, identify the domain, range, and asymptotes for y=1/2cscx-pi-1y=1/2cscx-pi-1?