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 2p, and tangent is a periodic function with period p.

Examples of Periodic Function

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

Video Examples: Periodic Functions Grade 11 mixed Lesson 6 1 11 20 12


Solved Example on Periodic Function

Ques: Identify the graph that does not represent a periodic function.

    Examples of  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.