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]}