Match each function with its graph in choices A–F.


y = tan (x - π )


A. <IMAGE> B. <IMAGE> C. <IMAGE>


D. <IMAGE> E. <IMAGE> F. <IMAGE>

Key Concepts

Tangent Function Properties

The tangent function, defined as tan(x) = sin(x)/cos(x), has specific properties including periodicity, asymptotes, and behavior around its vertical asymptotes. It is periodic with a period of π, meaning it repeats every π units. Understanding these properties is crucial for identifying the correct graph, especially how the function behaves as it approaches its asymptotes.

Phase Shift

A phase shift occurs when a function is horizontally translated along the x-axis. In the function y = tan(x - π), the graph of the tangent function is shifted π units to the right. Recognizing this shift is essential for accurately matching the function to its corresponding graph, as it alters the location of the function's key features, such as its asymptotes and intercepts.

Graphing Trigonometric Functions

Graphing trigonometric functions involves plotting key points, identifying asymptotes, and understanding the function's periodic nature. For the tangent function, it is important to note where the function is undefined (asymptotes) and how the graph behaves between these points. Familiarity with the general shape of the tangent graph helps in selecting the correct graph from the given options.