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.