How do you graph #y=4cot(3x-pi/4)-6#?

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Answer 1 · 2018-08-03T11:50:06

See graph and explanation.

#y = 4 cot ( 3x - pi/4 ) - 6, #

#3x - pi/4 ne #asymptotic #kpi#, k = 0, +-1, +-2, +-3, ...#

#rArr x ne # asymptotic # ( 4 k + 1 ) pi/12#

The period

= #pi/3# = x-spacing between two consecutive asymptotes..

Phase shift# = pi/12#

Vertical shift #= - 6#, for the axis.

See the graph, depicting all these aspects.
graph{((y+6)sin (3x-pi/4 )-4 cos ( 3x - pi/4))(y+6 +0x)(x+pi/4 +0.0001y)(x-pi/12+0.0001y)=0[-4 6 -18 6]}