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RnF - Coggle Diagram

- - - - Empty
      - Universal
    - - Symmetric
      - Transitive
      - Reflexive
  - - - How to know if a relation is a function
        
        Algebraically
        
        Independent and dependent variables
        
        Graphically
        
        Vertical line test
      - Terms
        
        Codomain = set B
        
        Range
        
        Domain = Set A
      - Algebra of function
        
        Substract
        
        Multiply
        
        Add
        
        Divide
    - - Constant inside function
      - Constant outside function
      - Modulus
      - GIF
      - operations
        
        Stretch
        
        Shift
        
        Squeeze
        
        Flip
        
        Horizontal
        
        Vertical
    - - Transcedental
        
        Exponential
        
        f(x) = a^x where a>1 and x e R
        
        TF
        
        tanx
        
        cosecx
        
        range of asinx + bcosx
        
        secx
        
        cosx
        
        cotx
        
        sinx
        
        Inverse functions
        
        Log (inverse)
        
        ITF(Inverse)
        
        Periodic fun
      - Algebraic
        
        Piecewise function
        
        Signum
        
        Fractional
        
        GIF
        
        Modulus
        
        Function of the form f(x) max or min
        
        Polynomial
        
        Quadratic
        
        vertex : (-b/2a, -D/4a)
        
        Case 2: a<0
        
        Case 1 : a>0
        
        If odd then has range R
        
        If even then does not take all R values
        
        Rational
        
        f(x) = P(x)/Q(x)
      - Some basic/ Elementary functions
        
        Constant fun
        
        Square fun
        
        Cubic fun
        
        Reciprocal fun
        
        Identity fun
        
        Identical functions
        
        Condition for two fucntions to be identical
        
        Modulus fun
      - Based on
        
        Symmetry of curve
        
        Evevn and odd
        
        Even and odd extension
        
        Mappings
        
        One-one and many-one
        
        One - one
        
        Has distinct image in codomain
        
        Also called injective
        
        Many-one
        
        Two pre images with same image
        
        Methods to determine one one and many one
        
        Graphical
        
        at least on eline parallel to x-axis cutting graph in two points then many one else one one
        
        Differentiation
        
        For continuous function f`(x) > or < 0 for all x belongs to domain of fun then it is one one else many one
        
        Analytical
        
        f(x1) =/= f(x2) -> one one else many one
        
        Onto- Into
        
        Onto
        
        Also known as surjective
        
        Range of f is same as codomain
        
        Into
        
        Range is subset of codomain
        
        Methods to determine onto and into fun
        
        Independent -> dependent
        
        Explicit and Implicit
        
        Has boundded or not
        
        Bounded
        
        Unbounded
      - Others
        
        Composite
    - - Finding function
      - Finding value of function at some point
      - Some properties
  - - - Range

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RnF

Unbounded

Basics

Relations

Modulus

Inequalities

Number of relations

Types of relations

Functions

Definition and terms

Domain

Basics

Transformation of graphs

Types of fucntions

Co-domain

Inverse

Identity

Trivial

Equivalence

Empty

Universal

Symmetric

Transitive

Reflexive

How to know if a relation is a function

Terms

Transcedental

Range

Algebraically

Algebra of function

Algebraic

Some basic/ Elementary functions

Exponential

TF

Inverse functions

Piecewise function

Polynomial

Quadratic

Signum

Fractional

GIF

Modulus

Based on

Others

Symmetry of curve

Mappings

Independent -> dependent

Composite

Explicit and Implicit

One-one and many-one

Onto- Into

Evevn and odd

Substract

Multiply

Add

Divide

One - one

Many-one

Has distinct image in codomain

Also called injective

Two pre images with same image

Methods to determine one one and many one

Graphical

Differentiation

Analytical

f(x1) =/= f(x2) -> one one else many one

at least on eline parallel to x-axis cutting graph in two points then many one else one one

For continuous function f`(x) > or < 0 for all x belongs to domain of fun then it is one one else many one

Onto

Into

Methods to determine onto and into fun

click to edit

click to edit

Also known as surjective

Range of f is same as codomain

Range is subset of codomain

If odd then has range R

If even then does not take all R values

Rational

f(x) = P(x)/Q(x)

vertex : (-b/2a, -D/4a)

Case 2: a<0

Case 1 : a>0

click to edit

click to edit

Log (inverse)

ITF(Inverse)

tanx

cosecx

range of asinx + bcosx

secx

cosx

cotx

sinx

f(x) = a^x where a>1 and x e R

Function of the form f(x) max or min

click to edit

click to edit

Even and odd extension

Constant inside function

Constant outside function

Modulus

GIF

operations

Stretch

Shift

Squeeze

Flip

Horizontal

Vertical

Functional Equations

Finding function

Finding value of function at some point

Some properties

2^pq

Codomain = set B

Domain = Set A

Range

Graphically

Vertical line test

Independent and dependent variables

Constant fun

Square fun

Cubic fun

Reciprocal fun

Identity fun

Modulus fun

Identical functions

Condition for two fucntions to be identical

Periodic fun

click to edit

Has boundded or not

Bounded

Unbounded