How do you graph $y = 4 cot (3 x - \frac{π}{4}) - 6$ $y=4cot(3x-pi/4)-6$ ?

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Answer 1 · 2018-08-03T11:50:06

See graph and explanation.

$y = 4 cot (3 x - \frac{π}{4}) - 6,$ $y = 4 cot ( 3x - pi/4 ) - 6,$

$3 x - \frac{π}{4} \neq$ $3x - pi/4 ne$ asymptotic $k π$ $kpi$ , k = 0, +-1, +-2, +-3, ...#

$\Rightarrow x \neq$ $rArr x ne$ asymptotic $(4 k + 1) \frac{π}{12}$ $( 4 k + 1 ) pi/12$

The period

= $\frac{π}{3}$ $pi/3$ = x-spacing between two consecutive asymptotes..

Phase shift $= \frac{π}{12}$ $= pi/12$

Vertical shift $= - 6$ $= - 6$ , 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]}

How do you graph y=4cot(3x−π4)−6y=4cot(3x-pi/4)-6?