Modulus graphs of tangent

Applying output modulus reflects negative tangent branches upwards but cannot create a value at an undefined input. Vertical asymptotes remain vertical asymptotes. Find where the inner tangent is undefined and split the drawing there. Find its zeros and useful endpoint values. Determine signs on each branch and reflect negative portions. For y=|tan x|, 0 <= x <= pi, exclude x= pi2; zeros are 0,pi, and the branch just right of pi2 reflects upwards. Check: never join across an asymptote. A factor inside the argument changes asymptote locations: tan2x is undefined at x= pi4, 3pi4 on [0,pi].