Signum Function

1. Signum function. Definition: $f(x)=\text{sgn}(x)$ is the piecewise function $f(x)=\begin{cases}-1, & x<0\\ 0, & x=0\\ 1, & x>0\end{cases}$ (Fig. 6.38). Domain: $R$; Range: $\{-1,0,1\}$.

Properties: (1) For $x>0$, the graph is the horizontal line $y=1$; for $x<0$, the graph is the horizontal line $y=-1$. (2) Since $f(0)=0$, the point $(0,0)$ is shown as a filled/black disc, whereas the points $(0,-1)$ and $(0,1)$ (which the two horizontal pieces wo …