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
The asymptotes for 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]}
