Periodic Function
Definition of Periodic Function

• A Function that repeats itself after a specific period of time is called a Periodic Function.

More about Periodic Function

• For a periodic Function g(x) with period a, g(x + a) = g(x).
• The trigonometric Functions, such as sine and cosecant are periodic functions with period 2π, and Tangent is a periodic Function with period π.

Examples of Periodic Function

• The hands of a clock show periodic behavior with time as variable.
• The seasons in year show a periodic behavior.

Solved Example on Periodic Function

Identify the Graph that does not represent a periodic function.

Choices:
A. Graph 1
B. Graph 3
C. Graph 4
D. Graph 2
Correct Answer: D
Solution:
Step 1: A Function that repeats itself after a specific period of time is called a Periodic Function.
Step 2: Among the graphs shown, observe that Graphs 1, 3, and 4 are periodic.
Step 3: Graph 2 is a parabola. Hence, Graph 2 does not represent a periodic function.

Related Terms for Periodic Function

• Function
• Period
• Time
• Trigonometric Functions

Additional Links for Periodic Function

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