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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.
  1. Start by plotting the midline:
  2. Now go left or right along the midline using the phase shift to get the center of the period at .
  3. From here, go left and right half of the period to find the ends of the period and put the vertical asymptotes.
  4. Dividing the period into quarters, we can get the 3 key points for graphing. (on the basic graph these are , , and .
  5. Finally Sketch the curve. It should be smooth and approach the asymptotes on both ends.