When thinking about the tangent function, here are the main points to keep in mind:
The graph of is shown here.
For graphing general tangent functions, we can adopt strategies similar to those used for graphing sines and cosines. The general form of the tangent function is
To get the general shape, place vertical asymptotes at the -values that satisfy
Other vertical asymptotes then repeat with the same spacing.
The "middle" of a period is the midpoint of your -values above.
represents a vertical shift.
is a scale factor (similar to amplitude). If , the graph is flipped about the -axis.
To graph any other trig function, we will first graph the corresponding reciprocal function, place vertical asymptotes at all zeros, and think about reciprocal values. It's actually pretty easy to do this once we've master sine, cosine, and tangent.
Rather than explain in writing, we will do lots of examples.