**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 2
*π*, 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