REPRESENTATION OF FUNCTIONS
About the topic "Representation of functions"
Representation of functions :
Here we are going to see "How to represent a function"
A function can be represented in the following four ways.
(i) A set of ordered pairs :
Let f : A ---> B
The set f = { (a , b) / a ∈ A and b ∈ B } of all ordered pairs represents the function
(ii) A table :
The elements of A and their respective images under f can be given in the form of a table.
(iii) An arrow diagram :
An arrow diagram indicates the elements of the domain of f and their respective images by means of arrows.
(iv) A graph :
The ordered pairs in the collection f are plotted as points (x, y) in the x-y plane. The graph of f is the totality of all such points.
Example :
Let A = { 0, 1, 2, 3 } and B = { 1, 3, 5, 7, 9 } be two sets. Let f : A ---> B be a function given by f (x) = 2x + 1. Represent this function as (i) a set of ordered pairs (ii) a table (iii) an arrow diagram and (iv) a graph.
Solution :
(i) A set of ordered pairs :
Here "x" ------> elements of A and f(x) ------> elements of B
Then, we have
f(0) = 2(0) + 1 = 0 + 1 = 1 -------> (0, 1)
f(1) = 2(1) + 1 = 2 + 1 = 3 -------> (1, 3)
f(2) = 2(2) + 1 = 4 + 1 = 5 -------> (2, 5)
f(3) = 2(3) + 1 = 6 + 1 = 7-------> (3, 7)
The given function f can be represented as a set of ordered pairs as
f = { (0, 1), (1, 3), (2, 5), (3, 7) }
(ii) A table :
Let us represent f using a table as shown below.
(iii) An arrow diagram :
(iv) A graph :
If the order pairs are written as points in the form (x, y), we will get the points (0, 1), (1, 3), (2, 5) and (3, 7).
These points are plotted on the x-y plane as shown below.
The totality of all points represent the graph of the function.
After having gone through the stuff given above, we hope that the students would have understood "Representation of functions".
Apart from the stuff given above, if you want to know more about "Representation of functions", please click here
If you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Finding Equation of Parallel Line
Feb 20, 20 03:09 AM
Finding Equation of Parallel Line - Concept and examples with step by step solution
-
Discount Problems in Profit and Loss
Feb 19, 20 04:35 AM
Discount Problems in Profit and Loss - Examples with step by solution
-
Find the Selling Price if we Want to Make a Given Profit or Loss
Feb 15, 20 06:47 AM
Find the Selling Price if we Want to Make a Given Profit or Loss - Example problems with step by step solution
