Sections:

Graphing Trigonometric Functions, Page 7

Properties of the Tangent Function

Now that you know what the asymptotes of the tangent function are, you can determine the properties of the graph f(x) = tan(x).

  • The period is Pi.
  • The domain is the set of all real numbers (All Real Numbers), except n times pi over two, where n is any odd integer, positive or negative. 

    Example: pi/2, 3pi/2, 5pi/2, etc.
  • The range is the set of all real numbers (All Real Numbers).
  • The x-intercepts occur at n times pi, where n is any integer.
  • The y-intercept is 0.
  • The asymptotes are at x equals n times pi over two, where n is any odd integer. 

Notice that there are no max or min properties, due to the asymptotes.