Step 1

Piecewise functions are functions which are defined by multiple fuction for different disjoint subdomain.

Example : consider signum function, it has domain \(\left(−\propto,\propto\right)\) and is defined as :

\(Sgn(x)=\begin{cases}-1\ if\ x<0\\0\ if\ x=0\\1\ if\ x>0 \end{cases}\)

Practical applications in which piecewise function is used :

Example 1 : Taxi fare system - If the distance on the meter is within 1 km than \(\$5\) is taken and for further each kilometer \(\$2\) is taken. This scenario depicts peicewise nature.

Step 2

Example 2 : The scolarship program - If your annual income is less than \(\$10000\) than full scholarship of \(\$1000\) will be given otherwise no scholarship will be given. This scenario also have piecewise nature.

Piecewise functions are functions which are defined by multiple fuction for different disjoint subdomain.

Example : consider signum function, it has domain \(\left(−\propto,\propto\right)\) and is defined as :

\(Sgn(x)=\begin{cases}-1\ if\ x<0\\0\ if\ x=0\\1\ if\ x>0 \end{cases}\)

Practical applications in which piecewise function is used :

Example 1 : Taxi fare system - If the distance on the meter is within 1 km than \(\$5\) is taken and for further each kilometer \(\$2\) is taken. This scenario depicts peicewise nature.

Step 2

Example 2 : The scolarship program - If your annual income is less than \(\$10000\) than full scholarship of \(\$1000\) will be given otherwise no scholarship will be given. This scenario also have piecewise nature.