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| Calculus
Contents A |
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Introduction
to Functions |
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 (a function of a function) |
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Inverse
function
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The
graph of a function |
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Function's
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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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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Transformations
of original or source function |
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How
some changes of a function's 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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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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Reciprocal
function |
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Transcendental functions |
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Exponential
and logarithmic functions, inverse functions |
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Trigonometric
(cyclometric) functions and inverse trigonometric functions (arc-functions) |
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The
graphs of the elementary functions |
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The
graphs of algebraic and transcendental functions |
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The
graphs of algebraic functions |
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The
graphs of the polynomial functions |
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The
source
or original polynomial function |
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Translating
(parallel shifting) of the polynomial function |
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Coordinates of translations
and their role in the polynomial expression |
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The
graph of the linear function |
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The
graph of the quadratic function |
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The
graphs of the cubic function |
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The
graphs
of the source cubic functions |
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The
graphs
of the translated cubic functions |
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The
graphs of the quartic function |
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The
graphs of the quartic functions types 1 and 2 |
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The
graphs of the quartic functions types 3/1 and 3/2 |
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The
graphs of the quartic functions types 4/1 . . . 4/6 |
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Sigma
notation of the polynomial |
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Coefficients of the source
polynomial in the form of a recursive formula |
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Coefficients
of the source polynomial function are related to its derivative
at x0 |
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Translated
power function |
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Translated
sextic function example
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Graphs
of rational
functions |
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Basic
properties of rational functions |
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Vertical asymptotes of
rational functions |
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Horizontal asymptote
of rational functions |
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The oblique or slant
asymptote of rational functions |
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The
graph of the reciprocal
function, equilateral or rectangular hyperbola |
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Translation of the reciprocal function, linear rational
function |
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Graphs of rational
functions examples |
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The graphs of transcendental functions |
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Exponential
and logarithmic functions are mutually inverse functions |
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The
graph of the exponential
function |
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The graph of
the
logarithmic
function |
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Trigonometric
(cyclometric) functions and inverse trigonometric functions (arc
functions) |
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The
graphs of the trigonometric
functions and inverse trigonometric functions or arc-functions |
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The graph of
the sine function |
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The graph of
the
cosine function |
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The graph of
the arc-sine function and the arc-cosine function |
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The
graph of the tangent function
and the
cotangent function |
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The
graph of the
arc-tangent function and the arc-cotangent function |
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The graph of
the
cosecant function |
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The graph of
the
secant function |
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The
graph of the
arc-cosecant and the
arc-secant function |
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