Functions
1.0 Definitions
2.0 Relation
3.0 Types of Relation
4.0 Functions
5.0 Standard Real Functions and their Graphical Representation
5.10 Reciprocal Function
5.1 Constant Function
5.2 Identity Function
5.3 Modulus Function
5.4 Greatest Integer Function or Floor Function
5.5 Smallest Integer Function or Ceiling Function
5.6 Fractional Part Function
5.7 Signum Function
5.8 Exponential Function
5.9 Logarithmic Function
5.11 Square Root or Radical Function
5.12 Square Function
5.13 Cube Function
5.14 Cube Root Function
6.0 Operations on Real Functions
7.0 Types of Functions
8.0 Composition of a Function
9.0 Inverse of a Function
5.7 Signum Function
5.1 Constant Function
5.2 Identity Function
5.3 Modulus Function
5.4 Greatest Integer Function or Floor Function
5.5 Smallest Integer Function or Ceiling Function
5.6 Fractional Part Function
5.7 Signum Function
5.8 Exponential Function
5.9 Logarithmic Function
5.11 Square Root or Radical Function
5.12 Square Function
5.13 Cube Function
5.14 Cube Root Function
The function $f$ defined by, $$f(x) = \left\{ \matrix{{{\left| x \right|} \over x}\;\;\;\;\;,\;when\;x \ne 0 \hspace{1em} \cr 0\;\;\;\;\;\;\;,\;when\;x = 0 \hspace{1em} \cr} \right.$$
$$f(x) = \left\{ \matrix{1\;\;\;\;\;,\;when\;x > 0 \hspace{1em} \cr 0\;\;\;\;\;,\;when\;x = 0 \hspace{1em} \cr - 1\;\;\;,\;when\;x < 0 \hspace{1em} \cr} \right.$$ is called the signum function.
The domain of this function is the set $R$ of all real numbers and the range is the set $[ - 1,0,1]$.
