Mathematics Lab Activity-6 Class XI

Mathematics Laboratory Activities on Relaton & Functons for class XI students Non-Medical. These activities are strictly according to the CBSE syllabus

Chapter - 2 | relations & functions

Activity - 6

Objective

To distinguish between a relation and  a function.

Material Required

Drawing board, coloured drawing sheets, scissors, adhesive, strings nails etc. 

Theory

Set : A set is a well defined collection of objects.

There are two methods of representing a set

i) Roster or tabular form:

In this form all elements of a set are listed and are separated by commas and are then enclosed within braces {}. For example:  Set of all vowels in the English alphabet is

V =  {a, e, I, o, u}.

ii) Set-builder form

In this form, all the elements of a set possess a single common property, which is not possessed by any element outside the set. For example: set of all vowels in English alphabet is written as:  V = {x : x is a vowel in the English alphabet}

Empty Set: A set which does not contain any element is called an empty set or the null set or the void set. It is denoted by the symbol ф  or { }.

Subset: A set A is said to be the subset of a set B, if every element of A is also an element of B. 

Procedure

 1. Take a drawing board and paste a colored sheet on it.

2. Take a white drawing sheet and cut out a rectangular strip of size 5cm x 3cm and paste it on the left side of the drawing board.

3. Fix three nails on the strip and mark them as a, b and c as shown in fig. 6.1

Figure 6.1 

4. Cut out another white rectangular strip of size 6cm x 4cm and paste it on the right hand side of the drawing board. Fix two nails on this strip and mark them as 1 and 2 as shown in fig. 6.2.

   Figure 6.2

5. Join nails on the left hand strip to the nails on the right hand strip by strings in different ways as shown in figure 6.3 to 6.6.

Figure 6.3 

Figure 6.4

 

Figure 6.5

Figure 6.6

6. The joining of nails in each figure constitutes different ordered pairs representing elements of a relation.

Observations

1. The ordered pairs in fig. 6.3 are : (a, 1), (a, 2), (b, 1), (b, 2), (c, 2). These ordered pairs constitute a relation  but not a function. Because ordered pair (a, 1), (a, 2) have same first element a and ordered pair (b, 1), (b, 2) have same first element b.

2. The ordered pairs in fig. 6.4 are : (a, 1), (b, 1), (c, 1) are constitute a relation as well as a function.

3. The ordered pairs in fig. 6.5 are : (a, 2), (b, 2), (c, 2). These ordered pairs constitute a relation as well as a function.

4. The ordered pairs in fig. 6.6 are : (b,1), (c, 2). These ordered pairs do not represent a function because element 'a' in first set do not have their image in second set. ButtThese ordered pair represents a relation.

Note: Every function is a relation but every relation need not to be a function.

Result

We have shown the difference between a relation and a function by using arrow diagrams.

Applications

This types of activities can be used to demonstrate different types of functions such as constant function, identity function, injective functions and surjective functions.

VIVA – VOICE

Q. 1. What is an identity function?

Ans. A function that always returns a same value that was used as its argument is called an identity function.

Q. 2. What is a constant function?

Ans. A function whose value is the same for all the elements of its domain is called a constant function.

Q. 3. What is a polynomial function?

Ans. A function f : R → R is said to be a polynomial function if for each x in R, y = f(x) = a₀ + a₁x + a₂x² + ……..a_n xⁿ ,  where n is a non negative integer and a₀, a₁, a₂ ,…… a_n ∈ R

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