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Pre-calculus
Contents D |
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Functions |
Introduction
to Functions |
Function definition, notation and
terminology |
Domain, range and
codomain |
Evaluating
a function |
Composition
of functions (a function of a function) |
Inverse
function
|
The
graph of a function |
Functions
behavior, properties
and characteristic points of the graph |
Domain
and range |
Roots or zero function
values, x-intercepts, y-intercepts |
Increasing/decreasing
intervals |
The
instantaneous
rate of change or the derivative |
Continuity and discontinuity |
Vertical,
horizontal and oblique or slant asymptotes |
Stationary
points and/or critical points |
Turning points (extremes, local or relative
maximums
or minimums) |
Inflection points and intervals of concavity |
Symmetry
of a function, parity - odd and even functions
|
Transformations
of original or source function |
How
some changes of a function notation affect the
graph of the function |
Translations
of the graph of a function
|
Reflections
of the graph of a function |
Types
of functions - basic classification |
Algebraic functions
and Transcendental functions |
Algebraic functions |
The
polynomial function |
Rational
functions |
Reciprocal
function |
Transcendental functions |
Exponential
and logarithmic functions, inverse functions |
Trigonometric
(cyclometric) functions and inverse trigonometric functions (arc-functions) |
The
graphs of the elementary functions
|
The
graphs of algebraic and transcendental functions |
The
graphs of algebraic functions |
The
graphs of the
polynomial functions |
The
source
or original polynomial function |
Translating
(parallel shifting) of the polynomial function |
Coordinates of translations
and their role in the polynomial expression |
The
graph of the linear function |
The
graph of the quadratic function |
The
graphs of the cubic function |
Graphing
cubic functions |
Graphing
translated
cubic function |
The
graphs of the quartic function |
Graphing
quartic
functions |
Graphing
translated quartic
function |
Translated
power function |
The
graphs of rational functions |
Basic
properties of rational functions |
The
graph of the reciprocal
function, equilateral or rectangular hyperbola |
Translation of the reciprocal function, linear rational
function |
The graphs of transcendental functions |
Exponential
and logarithmic functions are mutually inverse functions |
The
graph of the exponential
function |
The graph of
the
logarithmic
function |
Trigonometric
(cyclometric) functions and inverse trigonometric functions (arc
functions) |
The
graphs of the trigonometric
functions and inverse trigonometric functions or arc-functions |
The graph of
the sine function |
The graph of
the
cosine function |
The graph of
the arc-sine function and the arc-cosine function |
The
graph of the tangent function
and the
cotangent function |
The
graph of the
arc-tangent function and the arc-cotangent function |
The graph of
the cosecant function |
The graph of
the
secant function |
The
graph of the
arc-cosecant and the
arc-secant function |
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Pre-calculus Contents |
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