Signum Function
Signum function helps determine the sign of the real value function, and attributes +1 for positive input values of the function, and attributes 1 for negative input values of the function. The signum function has numerous applications in physics, engineering, and is prominently used in Artificial Intelligence, for predictions.
Let us learn more about signum function, the graph of signum function, and the applications of signum function.
1.  What Is Signum Function? 
2.  Graph of Signum Function 
3.  Applications of Signum Function 
4.  Examples of Signum Function 
5.  Practice Questions on Signum Function 
6.  FAQs on Signum Function 
What Is Signum Function?
The signum function simply gives the sign for the given values of x. For x value greater than zero, the value of the output is +1, for x value lesser than zero, the value of the output is 1, and for x value equal to zero, the output is equal to zero. The signum function can be defined and understood from the below expression.
The signum function is an odd function and is different from the trigonometric function of sine function.
Graph of Signum Function
The graph of signum function has two horizontal lines, parallel to the xaxis. Part of the line is parallel to the positive xaxis in the first quadrant and it represents the outputs of all the positive x values. And part of the line is parallel to the negative xaxis, in the third quadrant, and it represents the output of the negative x values.
The domain for a signum function includes all the real numbers and is represented along the xaxis, and the range of the signum function has only two values, +1, 1, represented on the yaxis.
Applications of Signum Function
The signum function has numerous applications in other areas of maths, physics, engineering, and in numerous areas of daytoday life. The following are some of the important applications of signum function.
 The signum function helps in extracting the sign of the real number.
 The signum function when applied to a complex number, helps to project it on the unit circle.
 The integration of a signum function gives a line inclined positively or negatively with the xaxis.
 The application of probability for a signum function predicts the happening or not happening of an event.
 The concept of signum function can be prominently used in any of the onoff function switches. The switches can be programmed for on or off, based on the defined input values, or the variation in the input value.
 The application of the signum function can be observed in a thermostat. Above a certain temperature the system is turned on and it starts cooling and below a certain temperature the system is turned off and it stops cooling.
Related Topics
The following topics help in better understanding of signum function.
Examples on Signum Function

Example 1: Show that the signum function \(f(x) =\begin{bmatrix}+1 & if &x > 0\\1 & if& x < 0\\0 & if& x = 0\end{bmatrix}\) is a constant function for all positive values of x.
Solution:
The given signum function is \(f(x) =\begin{bmatrix}+1 & if &x > 0\\1 & if& x < 0\\0 & if& x = 0\end{bmatrix}\).
Let us take a few positive values as the domain of this function x = {2, 3, 5}.
Applying these values for the signum function we have f(2) = +1, f(3) = +1, f(5) = +1.
Here we see that the range or the answer for all the positive values of x is always +1, which is a constant value.
Therefore a signum function is a constant function for all positive values of x.

Example 2: Find the output for the following values of x, using the signum function \(f(x) =\begin{bmatrix}+1 & if &x > 0\\1 & if& x < 0\\0 & if& x = 0\end{bmatrix}\).
x = {4.93, 7.66, 0, 11, 4.2, 3.33333, 5.10}
Solution:
Here we use the following signum function to find the output, for the input values of x.
\(f(x) =\begin{bmatrix}+1 & if &x > 0\\1 & if& x < 0\\0 & if& x = 0\end{bmatrix}\)
x = {4.93, 7.66, 0, 11, 4.2, 3.33333, 5.10}
Output = {+1, +1, 0, +1, 1, +1, 1}
FAQs on Signum Function
What Is Signum Function?
Signum function helps determine the sign of the real value function, and attributes +1 for positive input values of the function, and attributes 1 for negative input values of the function. For x value greater than zero, the value of the output is +1, for x value lesser than zero, the value of the output is 1, and for x value equal to zero, the output is equal to zero.
\(f(x) =\begin{bmatrix}+1 & if &x > 0\\1 & if& x < 0\\0 & if& x = 0\end{bmatrix}\)
This above expression represents the signum function.
How Do You Write a Signum Function?
The signum function is written as follows. It gives three possible outputs. It gives an output of +1 for x values greater than zero, an output of 1 for x values lesser than zero, and an output of zero for x values of zero.
What Is the Range of Signum Function?
The range of the signum function only includes the set of three values of 1, 0 and +1. For all the different input values of the x in the signum function of f(x), the range is only 1, 0, and +1.
Range of Signum Function = {1, 0, +1}
Can the Signum Function be written as an invertible function?
The signum function is not invertible. The 1 or +1 inputs for the inverse function cannot result in giving back the initial input of x of the primary signum function.
What Is the Domain of a Signum Function?
The domain of a signum function includes all the real number values. The signum function takes inputs of positive values and negative values.
How to Graph the Signum Function?
The graph of a signum function is a line parallel to the xaxis. For positive real number inputs for the signum function, the graph is a line parallel to the positive xaxis and is drawn above the xaxis. And for negative real number input values for the signum function, the graph is a line parallel to the negative xaxis and is drawn below the xaxis.
What Is The Difference Between Signum Function And Sine Function?
The difference between a signum function and a sine function can be easily understood graphically. The graph of a signum function is a line parallel to the xaxis on either side of the origin, and the graph of a sine function is a waveform, which is passing through the origin. The signum function and sine function have the same domain of real numbers, but the range of signum function is either 1 or +1, and the range of the sine function is between 1 and +1.
What Are the Applications of Signum Function?
The signum function has numerous applications in physics, engineering, and is prominently used in Artificial Intelligence, for predictions. The applications in onoff switches, and in thermostats we can find the signum function. In artificial intelligence to classify a subject into two distinct categories, we use the signum function.
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