Chapter 13.1, Problem 1LC

Solution

Whether the function shown below is periodic or not. And if it is periodic find its period.

  

The graph of the function represents a periodic function of period $5$ .

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 repeats itself for $y-$ values between $x=1\text{ and }x=6$ . Therefore, the given graph represents a periodic function.

Now the period of the function is the horizontal length- the distance along the $x-$ axis of one complete cycle. Therefore period $\left(T\right)$ of the periodic function is evaluated as:

  $\begin{array}{c}T=6-1\\ =5\end{array}$

Conclusion:

The function represents a periodic function of period $5$ .