Chapter 3.8, Problem 49WE

To determine

To draw: To graph the given signum function in the interval of $3\le x\le 3$ .

Explanation of Solution

Given information:Signum function $s(x)=\left\{\begin{array}{l}1\text{if}x>0\\ 0\text{if}x=0\\ -1\text{if}x<0\end{array}\right\}$

Graph:

Since, the given function $s(x)=\left\{\begin{array}{l}1\text{if}x>0\\ 0\text{if}x=0\\ -1\text{if}x<0\end{array}\right\}$

Plot all this values on the graph, we get

  

Interpretation:From the graph it can be seen that when x> 0, the value is constant to 1 similarly, when x <0, the value is fixed to $-1$ and when $x=0$ , we get the value 0.

Signum function is different from the function $f(x)=\frac{x}{\left|x\right|}$ because this function is not defined in 0, whereas signum function is defined in 0.