Is signum function a continuous function or not - Maths - Continuity and Differentiability

Question

Is signum function a continuous function or not

Shashank Goyal · Accepted Answer

The function f: R → R defined by

f open parentheses x close parentheses equals open curly brackets table attributes columnalign left columnspacing 1 4ex end attributes row cell negative 1 comma end cell cell x less than 0 end cell row cell 0 comma end cell cell x equals 0 end cell row cell 1 comma end cell cell x greater than 0 end cell end table close

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