Q.Describe the graph of the signum function and state its domain and range.

These three standard real functions are each defined piecewise rather than by one algebraic expression. The modulus function $f(x)=|x|$ gives the non-negative magnitude of $x$ (domain $\mathbb{R}$, range $[0,\infty)$) and its graph is a V-shaped pair of $45°$ rays meeting at the origin. The signum function reduces $x$ to just its sign, $1$, $0$ or $-1$ (domain $\mathbb{R}$, range $\{-1,0,1\}$), graphed as three disconnected horizontal pieces. The greatest integer f …