Question

Find the point where the graph of the function sgn (x) 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.