Functions 15 2 CS708 1 Functions 15 2
- Slides: 90
Functions – (15 - 2) CS-708 1
Functions – (15 – 2 a) CS-708 2
Example – (15 - 3) CS-708 3
Solution – (15 – 3 a) CS-708 4
Solution – (15 – 3 b) CS-708 5
Solution – (15 – 3 c) CS-708 6
Function – (15 - 5) CS-708 7
Remarks – (15 – 5 a) CS-708 8
Arrow Diagram of a Function – (15 - 6) CS-708 9
Example – (15 – 6 a) CS-708 10
Example – (15 – 6 b) CS-708 11
Nonfunction – (15 - 7) CS-708 12
Range of a Function – (15 - 8) CS-708 13
Remarks – (15 – 8 a) CS-708 14
Exercise – (15 - 9) CS-708 15
Exercise – (15 – 9 a) CS-708 16
Solution – (15 – 9 b) CS-708 17
Graph of a Function – (11 - 11) CS-708 18
Graph of a Function – (15 – 11 a) CS-708 19
Graph of a Function – (15 – 11 b) CS-708 20
Vertical Line Test – (15 - 12) CS-708 21
Example – (15 - 13) CS-708 22
Solution – (15 – 13 a) CS-708 23
Solution – (15 – 13 b) CS-708 24
Exercise – (15 - 15) CS-708 25
Exercise – (15 – 15 a) CS-708 26
Exercise – (15 – 15 b) CS-708 27
Exercise – (15 - 17) CS-708 28
Exercise – (15 – 17 a) CS-708 29
Exercise – (15 – 17 b) CS-708 30
Exercise – (15 - 18) CS-708 31
Solution – (15 – 18 a) CS-708 32
Functions Not Well Defined – (15 - 20) CS-708 33
Solution – (15 – 20 a) CS-708 34
Solution – (15 – 20 b) CS-708 35
Exercise – (15 - 21) CS-708 36
Solution – (15 – 21 a) CS-708 37
Solution – (15 - 22) CS-708 38
Binary Operations – (15 - 28) CS-708 39
Example – (15 – 28 a) CS-708 40
Injective Function or One-To-One Function – (16 - 2) CS-708 41
Arrow Diagram – (16 – 2 a) CS-708 42
Function not One-to-One – (16 - 3) CS-708 43
Example – (16 - 4) CS-708 44
Example – (16 – 4 a) CS-708 45
Example – (16 – 4 b) CS-708 46
Example – (16 – 4 c) CS-708 47
Example – (16 – 4 d) CS-708 48
Example – (16 – 4 e) CS-708 49
Example – (16 - 8) CS-708 50
Example – (16 - 9) CS-708 51
Solution – (16 – 9 a) CS-708 52
Example – (16 - 10) CS-708 53
Graph of One-To-One Function – (16 11) CS-708 54
Example – (16 – 11 a) CS-708 55
Surjective Function or Onto Function – (16 - 12) CS-708 56
Subjective Function or Onto Function – (16 – 12 a) CS-708 57
Function not Onto – (16 – 13) CS-708 58
Example – (16 - 14) CS-708 59
Solution – (16 – 14 a) CS-708 60
Example – (16 – 15) CS-708 61
Solution – (16 - 16) CS-708 62
Solution – (16 – 16 a) CS-708 63
Example – (16 – 20) CS-708 64
Solution – (16 – 20 a) CS-708 65
Solution – (16 – 20 b) CS-708 66
Bijective Function – (16 - 24) CS-708 67
Example – (16 – 24 a) CS-708 68
Example – (16 - 25) CS-708 69
Graph of Bijective Function – (16 - 27) CS-708 70
Graph of Bijective Function – (16 – 27 a) CS-708 71
Identity Function – (16 - 28) CS-708 72
Example – (16 – 28 a) CS-708 73
Constant Function – (16 – 30) CS-708 74
Example – (16 – 30 a) CS-708 75
Equality of Functions – (17 - 2) CS-708 76
Example – (17 – 2 a) CS-708 77
Example – (17 – 2 b) CS-708 78
Example – (17 - 3) CS-708 79
Solution – (17 – 3 a) CS-708 80
Inverse of a Function – (17 - 4) CS-708 81
Inverse of Injective Function – (17 - 5) CS-708 82
Inverse of Surjective Function – (17 - 6) CS-708 83
Inverse of Bijective Function – (17 -7) CS-708 84
Inverse Function – (17 - 8) CS-708 85
Arrow Diagram – (17 – 8 a) CS-708 86
Example – (17 - 9) CS-708 87
Example – (17 - 11) CS-708 88
Example – (17 – 11 a) CS-708 89
Example – (17 – 11 b) CS-708 90