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