Graphical Representation of a Function

The function f : R - {0} → R is represented in the graph such that the x co-ordinate represents the independent variable and the y co-ordinate represents the dependent variable. The graph of the function shows various properties of the function directly and more clearly. The limiting case of the graph of the function is represented by an asymptote:


Asymptote is a straight line to which graph of the function approaches at infinity but does not exactly touch it as shown in figure shown above.

  Coordinate axis x = 0 is asymptotes to the graph of y ­­= 1/x.

We consider some examples of functions and their graphs






A Constant Function

f : R → {c}

defined by f{x} = c



The Identity Function

f : R → R

defined by f(x) = x



The Absolute Value Function

f : R → [0, ∞)

defined by f(x) = |x|



The Exponential Function

f : R → (0, ∞)

defined by f(x) = ex



The Natural Logarithmic

f: (0, ∞) → R

defined by f(x) = In x



The Greatest Integer Function

f : R → Z

defined by f(x) = [x]

the greatest integer < x



The Fractional part of x

f : R → R

defined by f(x) = {x}



Polynomial Functions

f(x) = a0xn + a1xn-1 + .... + an-1 x + an

where a0, a1, ......, an are real numbers, a0 ≠ 0.


Rational Functions

f(x) = p(x)/q(x), where p(x) and q(x) are polynomials in x. Domain is R - {x : q(x) = 0}

10. Trigonometric or Circular Functions:
11. Inverse circular Functions
Register for online classroom programmes targeting IIT JEE 2010 and 2011. You can also participate in the online tests conducted by askIITians and also give answers in AQAD ( A Question A Day) to get a number of benefits in the online live classroom courses. Visit to read online Study material for IIT JEE and AIEEE preparation absolutely free.

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


Sign Up with Facebook

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!”

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 →...

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...

Inverse Function

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

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...

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

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

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 =...

Solved Examples Part-1

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

Increasing or Decreasing Function

Increasing or decreasing function The function f...

Introduction to Functions

Introduction to Functions Definition of Function:...

Cartesian Product

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