Question

Select the correct options related to the signum function $f\left(x\right)=\text{sgn}\left(x\right).$

• A. Range of $f\left(x\right)$ is $[-1,1]$
• B. Range of $f\left(x\right)$ is $\{-1,0,1\}$
• C. Range of $f\left(x\right)$ is $R$
• D. Domain of $f\left(x\right)$ is $R$

Answer 1

Answer: (B), (D)

Domain of $f\left(x\right)$ is $R$

Given: $f\left(x\right)=\text{sgn}\left(x\right)$
Now, we know that the signum function is defined as:
$\mathrm{sgn}\left(x\right)=(\begin{array}{c}\frac{x}{\left|x\right|};x\ne 0\\ 0;x=0\end{array}$And we can draw the graph as:


Thus, we can conclude:
Domain of $f\left(x\right)\text{is}R$
And it's Range is $\{-1,0,1\}.$