Explain Signum function

The function fR → defined by
 

 
 

is called the signum function. The domain of the signum function is and the range is the set 

 

{−1, 0, 1}. The graph of the signum function is given below.


 

In the graph, f(x) is represented along y-axis.


Now, from the definition of signum function, it is clear that value of f(x)=0 only when x=0.

When we take x>0, value of the function becomes 1 and when we take x<0, the value of f(x) 

becomes -1. To represent it on the graph, we use a small circle at x=0,y=1 and x=0, y=-1 to 

make ot clear that the value of function f(x) is 0 at x=0, as we have x>0, value of f(x) becomes 

1 and when x<0, value of f(x) becomes -1.

  • -1
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