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Welcome to
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Relations & Functions
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, Table of contents
Session 01 03 Session 03 46 Session 06 120
Ordered Pair 04 Identity function (𝑓(𝑥)=𝑥) 47 Properties of Logarithmic function 121
Cartesian Product of sets (𝐴×𝐵) 06 Rational Function 49 Number of Digits & Number of Zeroes 127
Number of elements in Cartesian 09 Modulus function 51 Logarithmic Inequalities 130
Product of sets
Turning Point 55 Greatest Integer Function 133
Relation 13
Properties of Modulus 58 Fractional part Function 142
Domain 14
Total number of Relations 16 Session 04 66
Inverse of a Relation 17 Steps for Plotting the Graph 69 Session 07 151
Void Relation 18 Properties of Modulus Inequality 82 Graphical Transformation : 152
Universal Relation 19 Vertical Stretch
Two bracket inequality 84
Graphical Transformation : 166
Identity Relation 20
Reflection of 𝑦 =𝑓(𝑥) in 𝑥 − axis
Session 05 95 Graphical Transformation : 168
Session 02 22
Signum Function 96 Reflection of 𝑦 =𝑓(𝑥) in 𝑦− axis
Function 29
Graphical Transformation : 178
Exponential Function 99
Vertical Line Test 31 𝑦 =𝑓(|𝑥|) type
Domain, Co-domain and range 32 Logarithmic Function 101
of a function Properties of Logarithmic function 103
Real Function 36
Standard Functions 38
Polynomial Function 39
Constant Function 43
, Session 1
Introduction to Relations and
Its Types
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, Key Takeaways
Ordered Pair:
● Listing of two objects or elements in a specific order.
● If 𝑎 is the first element and 𝑏 is the second element then
ordered pair is represented as 𝑎, 𝑏 .
● 𝑎, 𝑏 , (𝑏, 𝑎) are 2 different ordered pairs.
● If three elements are written in the form (𝑎, 𝑏, 𝑐) then it is
known as ordered triplet.
Equality of Ordered Pair:
● Two ordered pairs are equal if and only if the corresponding
first and second components are equal.
● 𝑎1 , 𝑏1 = 𝑎2 , 𝑏2 ⇔ 𝑎1 = 𝑎2 and 𝑏1 = 𝑏2
Return To Top
Welcome to
x
0
Relations & Functions
x
2 y
3
3
4
5
6
7
8
, Table of contents
Session 01 03 Session 03 46 Session 06 120
Ordered Pair 04 Identity function (𝑓(𝑥)=𝑥) 47 Properties of Logarithmic function 121
Cartesian Product of sets (𝐴×𝐵) 06 Rational Function 49 Number of Digits & Number of Zeroes 127
Number of elements in Cartesian 09 Modulus function 51 Logarithmic Inequalities 130
Product of sets
Turning Point 55 Greatest Integer Function 133
Relation 13
Properties of Modulus 58 Fractional part Function 142
Domain 14
Total number of Relations 16 Session 04 66
Inverse of a Relation 17 Steps for Plotting the Graph 69 Session 07 151
Void Relation 18 Properties of Modulus Inequality 82 Graphical Transformation : 152
Universal Relation 19 Vertical Stretch
Two bracket inequality 84
Graphical Transformation : 166
Identity Relation 20
Reflection of 𝑦 =𝑓(𝑥) in 𝑥 − axis
Session 05 95 Graphical Transformation : 168
Session 02 22
Signum Function 96 Reflection of 𝑦 =𝑓(𝑥) in 𝑦− axis
Function 29
Graphical Transformation : 178
Exponential Function 99
Vertical Line Test 31 𝑦 =𝑓(|𝑥|) type
Domain, Co-domain and range 32 Logarithmic Function 101
of a function Properties of Logarithmic function 103
Real Function 36
Standard Functions 38
Polynomial Function 39
Constant Function 43
, Session 1
Introduction to Relations and
Its Types
Return To Top
, Key Takeaways
Ordered Pair:
● Listing of two objects or elements in a specific order.
● If 𝑎 is the first element and 𝑏 is the second element then
ordered pair is represented as 𝑎, 𝑏 .
● 𝑎, 𝑏 , (𝑏, 𝑎) are 2 different ordered pairs.
● If three elements are written in the form (𝑎, 𝑏, 𝑐) then it is
known as ordered triplet.
Equality of Ordered Pair:
● Two ordered pairs are equal if and only if the corresponding
first and second components are equal.
● 𝑎1 , 𝑏1 = 𝑎2 , 𝑏2 ⇔ 𝑎1 = 𝑎2 and 𝑏1 = 𝑏2
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