# Graphing the Tangent Function

The easiest way to graph a tangent function with transformations is to figure out what happens to the period where for the basic function ( ) after the transformations have been applied.

- Start by plotting the midline:
- Now go left or right along the midline using the phase shift to get the center of the period at
. - 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
, , and . - Finally Sketch the curve. It should be smooth and approach the asymptotes on both ends.

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