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.
A. Graph 1
B. Graph 3
C. Graph 4
D. Graph 2
Correct Answer: D
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.