Chapter 13, Problem 6E

Solution

To identify: The function is periodic or not and obtain the amplitude and period of function.

Periodic function.

Amplitude: $2$

Period: $2$

Given:

A graph as follows:

  

Concept used:

1. A periodic function's graph repeats along the horizontal axis and is symmetrical.

Explanation:

The function is periodic because the graph of the function is repeating itself and it is symmetric.

The period of the function is,

  $3-1=2$

The amplitude of the function is,

  $\begin{array}{c}\text{amplitude}=\frac{\left(\max -\min \right)}{2}\\ =\frac{\left(2-\left(-2\right)\right)}{2}\\ =2\end{array}$

The one way to identify the one cycle is to analyse the two points at the which the curve has maximum value. And the second way is to identify the cycle is to start from zero and observe when the curve reaches it position again.

Conclusion:

Hence, function is periodic. The amplitude of the function is $2$ and period is $2$ .