The easiest way to graph a tangent function with transformations is to figure out what happens to the period where [math]x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right][/math] for the basic function ([math]y=\tan x[/math]) after the transformations have been applied.[br][list=1][*]Start by plotting the midline: [math]y=d[/math][br][/*][*]Now go left or right along the midline using the phase shift to get the center of the period at [math]\left(c,d\right)[/math].[/*][*]From here, go left and right half of the period to find the ends of the period and put the vertical asymptotes.[/*][*]Dividing the period into quarters, we can get the 3 key points for graphing. (on the basic graph these are [math]\left(-\frac{\pi}{4},-1\right)[/math], [math]\left(0,0\right)[/math], and [math]\left(\frac{\pi}{4},1\right)[/math].[/*][*]Finally Sketch the curve. It should be smooth and approach the asymptotes on both ends.[br][/*][/list]