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

Step 1: By definition, $f(x)=-1$ for every $x<0$, $f(0)=0$, and $f(x)=1$ for every $x>0$.

Step 2: The graph is therefore three separate horizontal pieces: a ray at height $y=-1$ for $x<0$ (open circle at its right end, above the origin), a single filled point at the origin $(0,0)$, and a ray at height $y=1$ for $x>0$ (open circle at its left end, above the origin) — with a visible vertical gap between each piece at $x=0$. …

Split into the three cases $x<0$, $x=0$, $x>0$ from the definition, and describe/read …

• Drawing the pieces as joined into one continuous zig-zag line instead of three disconnected pieces. …