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| MATHEMATICS Formulas, Graphs,
Tables, . . . < High School to University Level > |
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CONTENTS G
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61
Functions
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Introduction
to functions
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Function definition, notation and
terminology
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Domain, range and
codomain
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Evaluating
a function
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Composition
of functions (or a function of a function)
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Inverse
function
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62
The
graph of a function
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Functions
behavior, properties
and characteristic points of the graph
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Domain and range
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Roots or zero function
values, x-intercepts, y-intercepts
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Increasing/decreasing
intervals
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The
instantaneous
rate of change or the derivative
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Continuity and discontinuity
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Vertical,
horizontal and oblique or slant asymptotes
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Vertical
asymptote
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Horizontal
asymptote
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Oblique or slant
asymptote
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63
Stationary
points and/or critical points
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Turning points (extremes, local or relative maximums
or minimums)
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Inflection points and intervals of concavity
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Symmetry
of a function, parity - odd and even functions
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64
Transformations
of original or source function
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How
some changes of a function notation affect the
graph of the function
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Translations
of the graph of a function
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Reflections
of the graph
of a function
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65
Types
of functions - basic classification
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Algebraic functions
and transcendental functions
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Algebraic
functions
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The
polynomial function
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Rational
functions
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Transcendental
functions
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Exponential
and logarithmic functions
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Trigonometric functions and
inverse trigonometric functions
(arc
functions)
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66
Polynomial and/or polynomial
functions and equations
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Definition
of a polynomial or polynomial function
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Polynomial function
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The
source
or the original polynomial function
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Translating
(parallel shifting) of the source polynomial function
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Coordinates of translations
and their role in the polynomial expression
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67
The general form
or translatable form of the polynomial
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Coordinates of translations and coefficients of the source
polynomial
functions formulas
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Sigma
notation of the polynomial
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Coefficients of the source
polynomial shown by a recursive formula
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Coefficients
of the source polynomial function are related to its derivative
at x0
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68
Factoring
polynomials and solving
polynomial equations by factoring
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Factoring
polynomials examples
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Vieta's
formulas, relations between coefficients and roots of a
polynomial
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Roots or zeros of
polynomial function
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69
Vieta's
formulas
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Polynomial
coefficients and roots relations example
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Quadratic
polynomial expressed by roots
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Cubic
polynomial expressed by roots
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Quartic
polynomial expressed by roots
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Cubic
polynomial expressed by roots example
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70
Translated monomial (or power)
function
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Even
power function
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Odd
power function
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Odd
translated power function example
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