Chapter 13, Problem 2CT

Solution

To find: Whether the graph of the function represents a periodic function or not. If it is periodic then find its period and amplitude.

  

The graph of the function doesn’t represent a periodic function, so its period is not defined. And the range of the function is not bounded so its amplitude doesn’t exist.

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.

The amplitude $\left(a\right)$ of a periodic function $a=\frac{1}{2}\left(y_{\max }-y_{\min }\right)$ where $y_{\max }\text{ and }{y}_{\min }$ is the maximum and minimum value of the function.

Calculation:

From the graph of the function, it can be interpreted that the function repeats itself for $y-$ values between any values of $\left(x\right)$ in one complete cycle. Therefore, the given graph represents a non-periodic function. So, its period is not defined.

Also, the maximum and minimum value of the function is doesn’t exist because its range is not bounded. So, its amplitude doesn’t exist.

Conclusion:

The graph of the function doesn’t represent a periodic function, so its period is not defined. And the range of the function is not bounded so its amplitude doesn’t exist.