Chapter 13.1, Problem 13PPSE

Solution

To find: Whether the function shown below is periodic or not and if it is periodic find the period.

  

The function doesn’t represent a periodic function.

Given:

The graph of the function is shown below.

  

Concept used: A periodic function is a function that repeats itself a pattern of outputs ( $y-$ values) at regular intervals where one complete pattern represents a cycle. The period of the function is the horizontal length- the distance along the $x-$ axis of one complete cycle.

Calculation:

From the graph of the function, it can be interpreted that the function doesn’t repeat itself for $y-$ values (outputs) for any regular interval. And, $y-$ values are not the same over any particular cycle. Therefore, the given graph doesn’t represent a periodic function. Hence its period is not defined.

Conclusion:

The function doesn’t represent a periodic function.