Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
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
S.No.
Function
Domain, Range and Definition
Graph
1.
A Constant Function
f : R → {c}
defined by f{x} = c
2.
The Identity Function
f : R → R
defined by f(x) = x
3.
The Absolute Value Function
f : R → [0, ∞)
defined by f(x) = |x|
4.
The Exponential Function
f : R → (0, ∞)
defined by f(x) = ex
5.
The Natural Logarithmic
f: (0, ∞) → R
defined by f(x) = In x
6.
The Greatest Integer Function
f : R → Z
defined by f(x) = [x]
the greatest integer < x
7.
The Fractional part of x
defined by f(x) = {x}
8.
Polynomial Functions
f(x) = a0xn + a1xn-1 + .... + an-1 x + an
where a0, a1, ......, an are real numbers, a0 ≠ 0.
9.
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 askIITians.com to read online Study material for IIT JEE and AIEEE preparation absolutely free.
To read more, Buy study materials of Set Relations and Functions comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Composite Functions Problem of finding out fog and...
Bounded and Unbounded Function Let a function be...
Set Theory Table of Content Set Union of Sets...
Greatest Integer Function The function f(x) : R...
Graphical Representation of a Function 10....
Constant Function and the Identity Function The...
Absolute Value Function The function defined as:...
Basic Transformations on Graphs Drawing the graph...
Exponential Function Exponential and Logarithmic...
Signum Function The signum function is defined as...
Explicit and Implicit Functions If, in a function...
Periodic Function These are the function, whose...
Even and Odd Function A function f(x) : X → Y...
Logarithmic Function We have observed that y = a x...
Invertible Function Let us define a function y =...
Functions Table of Content What are Functions?...
Increasing or Decreasing Function The function f...
Introduction to Functions Definition of Function:...
Inverse Function Let f : X → Y be a function...
Set, Relations and Functions – Solved...
Linear Function When the degree of P(x) and Q(x)...
Polynomial and Rational Function A function of the...
Relations Table of Content What do we mean by...
Composite Functions Another useful combination of...
Cartesian Product of Sets Table of Content Define...
Algebra of Functions Given functions f : D →...
Functions: One-One/Many-One/Into/Onto Functions...