# Monotonic Behavior of the Function

Functions are said to be monotonic if they are either increasing or decreasing in their entire domain, e.g.,

*f*(*x*) =*e*.^{x}*f*(

*x*) = log

*and*

_{e}x*f*(

*x*) = 2

*x*+ 3 are some of the examples of functions which are increasing, whereas

*f*(

*x*) = â€“

*x*

^{3},

*f*(

*x*) =

*e*

^{â€“x}and

*f*(

*x*) = cot

^{â€“1}

*x*are some of the examples of the functions which are decreasing. Functions which are increasing as well as decreasing in their domain are said to be non-monotonic, e.g.,

*f*(

*x*) = sin

*x*;

*f*(

*x*) =

*ax*

^{2}+

*b*x +

*c*and

*f*(

*x*) = |

*x*|, however in the interval ,

*f*(

*x*) = sin

*x*will be said to be increasing.