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All About Functions- For a Layman.pptx
The document explains functions as relations between sets where each element of one set (domain) corresponds to a unique element in another set (co-domain). It discusses various types of functions and their definitions, highlighting concepts such as input-output relationships and the importance of the domain in determining function behavior. Additionally, it includes examples and graphical representations to illustrate these concepts.
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All About Functions- For a Layman.pptx
- 1. All About Functions- fora Layman Dr Farhana Shaheen
- 2. Definition of aFunction Specific------ Layman What is the meaning of Function? An Event? Occasion? Or??? Where do we use this word “Function” other than Events? 8/17/2023 2
- 3. A Function isa Relation or a Link between two sets- X and Y What is a RELATION? A Father – Children Relation A Children- Father Relation A Student – Teacher Relation A Teacher – Student Relation…… and much more 8/17/2023 3
- 4. Example: A Father– Children Relation 8/17/2023 4
- 5. A Function isa Relation or a Link between two sets- X and Y, such that Each element of X has a unique element (image) in Y. 8/17/2023 5
- 6. Let’s Go forIce Creams… 8/17/2023 6
- 7. Three friends A,B and C plan to have Ice Cream Treat- The condition is EVERYONE Must Choose Only one Ice-Cream A B C 8/17/2023 7
- 8. Suppose that Achooses two, B chooses one and C refuse to have any- Rules violated? 8/17/2023 8
- 9. Three friends A,B and C plan to have Ice Cream Treat- The condition is EVERYONE Must Choose Only one Ice-Cream A B C 8/17/2023 9
- 10. Function is anInput-Output Machine 8/17/2023 10 Note: The Output DEPENDS upon the Input. Input is INDEPENDENT. But Input depends upon the MACHINE.
- 11. Examples of Functionsas Machines Every Machine has a Program 8/17/2023 11
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- 14. A Function isan Input-Output Machine y = f(x) (x, y are Dummy variables) 8/17/2023 14
- 15. Definition: Function A Functionis a rule (or relation) from a set X to a set Y such that each element of X has a unique element in Y. We denote it by y = f(x). The set X is called the Domain and Y is called the Co- domain. Set X is Independent and Y is Dependent. Each → Elements of Domain are not missed Unique → Elements of Domain are not repeated DOMAIN is Very Important 8/17/2023 15
- 16. Dependent and IndependentVariables Examples of Functions in one, two or more variables: Area of a Circle depends upon its Radius A(r) = 𝜋𝑟2 Area of a Rectangle depends upon its length and width. A(L,W) = LW Volume of a Cuboid depends upon its length, width and height. V(L,W,H) = LWH 8/17/2023 16
- 17. Example: Three friendsA, B, C, plan to have ice- creams. Suppose all of them choose Chocolate Ice-Cream. Rules violated? X → Y A B C 8/17/2023 17
- 18. Example: Three friendsA, B, C, plan to have ice- creams. Suppose each of them choose different Ice- Cream. What is this function called? X → Y A B C 8/17/2023 18
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- 20. Are these Functionsor Relations? 8/17/2023 20
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- 22. Representing Functions asset of Ordered pairs f = {(a, b), (c, d)} 8/17/2023 22
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- 24. Graphs of Functions 8/17/2023 24 Agraphic illustration conveys a stronger message than words —one picture is worth a thousand words.
- 25. To draw aGraph….. We Need to know its DOMAIN Why is it necessary to find the Domain of a Function? Where to begin with…. 8/17/2023 25
- 26. Concept of Domainand Range What is the difference between Co-domain and Range? Let my machine is Programmed to square every Input, and add 3 more units. So f(x) = 𝒙𝟐 + 𝟑. 8/17/2023 26
- 27. f(x) should beDEFINED on its Domain A function is said to be DEFINED on the Domain if its image exists on its values, and is not imaginary. i.e. images are real-valued. For example: f(x)= 1 𝑥 −3 does not exist at x = 3. Also f(x) = 𝑥 + 5 has imaginary values for x < -5. 8/17/2023 27
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- 32. Depends on the typeof function 8/17/2023 32
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- 39. Finding domain andRange from graph 8/17/2023 39
- 40. Finding domain andRange from graph 8/17/2023 40
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- 42. Note: Not everygraph is the graph of a function- 8/17/2023 42
- 43. Vertical Line Testfor a Graph to be the graph of a Function 8/17/2023 43
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- 46. Types of Functions Linear Function Log Function Polynomial Function Exponential Function Radical Function Rational Function Identity Function Constant Function Reciprocal Function Trigonometric Function Inverse Trigonometric Function Piecewise Function 8/17/2023 46
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- 48. Constant Function y=k. What is x =? 8/17/2023 48
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- 54. Polynomial Functions vsReciprocal Functions 8/17/2023 54
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- 62. Exponential Functions y= 𝑎𝑥 8/17/2023 62
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- 64. Logarithmic Functions y= log x /lnx 8/17/2023 64
- 65. Bracket Functions (StepCurve) 8/17/2023 65
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