Question

Find the point where the graph of the function $sgn\left(x\right)$ breaks or becomes discontinuous. (sgn is the signum function)

Answer 1

The function f: R → R defined by

$f\left(x\right)=\{\begin{array}{cc}1,& ifx>0\\ 0,& ifx=0\\ -1& ifx<0\end{array}$

is called the signum function.

The domain of the signum function is R and the range are the set {$-1,0,1$}

The graph of a signum function is

Signum function is discontinuous at $x=0$.