A typical graph of #tanx# has domain for all values of #x# except at #(2n+1)pi/2#, where #n# is an integer (we have asymptotes too here) and range is from #[-oo,oo]# and there is no limiting (unlike other trigonometric functions other than tan and cot). It appears like graph{tan(x) [-5, 5, -5, 5]}

The period of #tanx# is #pi# (i.e. it repeats after every #pi#) and that of #tanax# is #pi/a# and hence for #tan2x# period will be #pi/2#

Hencem the asymptotes for #tan2x# will be at each #(2n+1)pi/4#, where #n# is an integer.

As the function is simply #tan2x#, there is no phase shift involved (it is there only if function is of the type #tan(nx+k)#, where #k# is a constant. Phase shift causes graph pattern to shift horizontally to left or right.

The graph of #tan2x# appears like graph{tan(2x) [-5, 5, -5, 5]}