Draw the graph of |y| = tan x.

To graph the equation |y| = tan x, we need to understand the behavior of the tangent function and how the absolute value affects it.

Understanding the Tangent Function

The tangent function, tan x, has a periodic nature with a period of π. It has vertical asymptotes where the function is undefined, specifically at x = (π/2) + nπ, where n is any integer.

Graphing |y| = tan x

Since we are dealing with the absolute value, the graph will reflect any negative values of tan x above the x-axis. Here’s how to sketch it:

• Start by plotting the basic tan x graph, which oscillates between negative and positive infinity.
• Identify the vertical asymptotes at x = (π/2) + nπ.
• For every point where tan x is negative, reflect it across the x-axis to create the |y| = tan x graph.

Key Features of the Graph

The resulting graph will have the following characteristics:

• It will be symmetric about the x-axis due to the absolute value.
• It will have vertical asymptotes at the same locations as the tan x graph.
• The graph will repeat every π units.

Final Thoughts

By combining the properties of the tangent function with the absolute value, you create a unique graph that showcases both periodic behavior and symmetry. Make sure to label your axes and asymptotes clearly when you draw it!