Question

Define signum function draw its graph and find its domain and range

Answer 1

Step 1. Signum function.

The real function $f:P\to P$defined by

$\left\{\begin{array}{c}\frac{\left|f\left(a\right)\right|}{f\left(a\right)},\mathrm{if}a\ne 0\\ 0,\mathrm{if}a=0\end{array}\right\}=\left\{\begin{array}{c}1,\mathrm{if}x>0\\ -1,\mathrm{if}x<0\\ 0,\mathrm{if}x=0\end{array}\right\}$ is called the signum function or sign function.

• Domain of $f=P$
• Range of $f=1,0,–1$

Step 2.Graph for signum function

The function $f:R\to R$ defined by

$f\left(x\right)=\left\{\begin{array}{c}1,\mathrm{if}x>0\\ -1,\mathrm{if}x<0\\ 0,\mathrm{if}x=0\end{array}\right\}$ is called the signum function or sign function.

The graph of the signum function is given below

Hence,

The function $f:R\to R$ defined by $f\left(x\right)=\left\{\begin{array}{c}1,\mathrm{if}x>0\\ -1,\mathrm{if}x<0\\ 0,\mathrm{if}x=0\end{array}\right\}$ is called the signum function or sign function.

• Domain of $f=P$
• Range of $f=1,0,–1$

The graph of the signum function is: