Total Price: R

There are no items in this cart.
Continue Shopping

Increasing or decreasing function

The function f is said to be an increasing function in its domain D if

        ∀ x2 > x1 => f(x2) > f(x1); x1, x2 ε D       


However if

        ∀ x2 > x1 => f(x2) > f(x1), x1, x2 ε D       

The function 'f' is said to be strictly increasing

The function 'f' is said to be decreasing function in its domain D if

        ∀ x2 > x1 => f(x2) < f(x1); x1, x2 ε D                

However if

        ∀ x2 > x1 => f(x2) < f(x1); x1, x2 ε D

Then it said to be strictly decreasing.

Strictly increasing and decreasing functions are also called Monotonic Function.


        Is y = 2x + 3 increasing/decreasing function.


Since, ∀ x ε R, y ε R

        Therefore Df = R

Let x2 > x1; x1, x2 ε R

        =>     2x2 > 2x1

        =>     2x2 + 3 > 2x1 + 3

        =>     f(x2) > f(x1)

        =>     y = f(x) = 2x + 3 is strictly increasing function.


1. Are the following function increasing/decreasing?

        (a)    y = x3 + 8                 (b)    y = -2x + 4
Ans.  (a) Decreasing

        (b) Strictly decreasing 

You can participate in the online tests conducted by askIITians and also give answers in AQAD (A Question  A Day) just by visiting the website This will give you a number of benefits in the online live classroom courses targeting IIT JEE 2010 and 2011. Read online Study material for IIT JEE and AIEEE preparation absolutely free at


Contact askiitians experts to get answers to your queries by filling up the form given below:

We promise that your information will be our little secret. To know more please see our Privacy Policy
We promise that your information will be our little secret. To know more please see our Privacy Policy


Signing up with Facebook allows you to connect with friends and classmates already using askIItians. It’s an easier way as well. “Relax, we won’t flood your facebook news feed!”

Ask Experts

Have any Question? Ask Experts

Post Question

Related Resources
Composite Functions Part-2

Composite Functions Problem of finding out fog and...

Bounded and Unbounded Function

Bounded and Unbounded Function Let a function be...

Set Theory

Set Theory SET A set is a well-defined collection...

Algebra of Functions

Algebra of Functions Given functions f : D →...

Graphical Representation of a Function Part-1

Graphical Representation of a Function The...

Greatest Integer Function

Greatest Integer Function The function f(x) : R...

Graphical Representation of a Function Part-2

Graphical Representation of a Function...

Polynomial And Rational Function

Polynomial And Rational Function A function of the...

Constant Function and Identity Function

Constant Function and the Identity Function The...


INEQUALITIES The following are some very useful...

Basic Transformations on Graphs

Basic Transformations on Graphs Drawing the graph...

Exponential Function

Exponential Function Exponential and Logarithmic...

Signum Function

Signum Function The signum function is defined as...

Explicit and Implicit Functions

Explicit and Implicit Functions If, in a function...

Absolute Value Function

Absolute Value Function The function defined as:...

Periodic Function

Periodic Function These are the function, whose...

Even And Odd Function

Even And Odd Function A function f(x) : X → Y...

Logarithmic Function

Logarithmic Function We have observed that y = a x...

Linear Function

Linear Function When the degree of P(x) and Q(x)...

Composite Functions Part-1

Composite Functions Another useful combination of...

Invertible Function Part-1

Invertible Function Let us define a function y =...

Introduction to Functions

Introduction to Functions Definition of Function:...

Functions One-One/Many-One/Into/Onto

Functions: one-one/many-one/into/onto Functions...

Inverse Function

Inverse Function Let f : X → Y be a function...

Solved Examples Part-1

Download IIT JEE Solved Examples on Set, Relations...

Cartesian Product

Cartesian Product Let A and B are two non-empty...