How do you graph # y=5-tan2(x-pi)#?

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Answer 1 · 2018-08-14T13:44:29

See explanation and graph.

#y = 5 - tan ( 2 ( x - pi ) = 5 + tan ( 2pi - 2x ) = 5 - tan 2x#,

#2x ne# ( asymptotic zero of cos 2x ) ( 2k + 1 ) pi/2#

#rArr x ne ( 2k + 1 ) pi/4, k = 0, +-1, +-2, +-3, ...#

The period = #pi#/2.

Amplitude of #oo#-arm wave is 1/2( period ) = #pi/4#

Vertical shift is 5 #rArr# axis is y = 5.

See graph, depicting all these aspects.
graph{(y-5+tan (2x))(y-5)(x-pi/4+0.01+0.005y)(x+pi/4--0.05+.005y)=0[-6 6 0 10]}