Total Price: R

There are no items in this cart.
Continue Shopping

Absolute Value Function

The function defined as:


is called an absolute value function.

Note : √x2 = |x| ∀  x  ε R


The graph of an absolute value function is shown in the figure given above. Its properties are:

(i) An absolute value function is an even function

(ii) It is strictly increasing in [0, ∞) and strictly decreasing in (-∞, 0].

Illustration 12: Draw the graph of the following functions.

(a) y = |x - 1| + |x - 4|

(b) y = |sin x|

(c) y = sin |x|


(a) Note:  x - 1 = 0 => x = 1 and x - 4 = 0 => x = 4 i.e. y changes its definition at x =1 and x = 4.

        y = |x - 1| + |x - 4|

        let - ∞ < x < 1

        y = -(x - 1) - (x - 4) = -2x + 5

Now, let 1 < x < 4

        y = (x - 1) - (x - 4) = 3

Again, Let 4 < x

        y = (x - 1) + (x - 4) = 2x - 5


(b)    y = |sin x|

        y > 0 ∀ x ε R


(c)    y = sin |x|

        ∀ x > 0,                     y = sin x

        ∀ x < 0,                     y = sin (-x) = -sinx



IIT JEE study material is available online free of cost at Study Set Theory, Functions and a number of topics of Algebra at askIITians website and be a winner. We offer numerous live online courses for IIT JEE preparation - you do not need to travel anywhere any longer - just sit at your home and study for IIT JEE live online with

To know more about the study material of engineering and medical exams, please fill 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...

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 =...

Increasing or Decreasing Function

Increasing or decreasing function The function f...

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...