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College
algebra contents B
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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
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The Graph of a Function
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Functions
behavior, properties
and characteristic points of the graph |
Domain and range |
Roots or zero function
values, x-intercepts, y-intercepts |
Increasing/decreasing
intervals |
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
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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
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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 |
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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 |
The
graphs of the quartic function |
Translated
power function |
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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 |
Transcendental
Functions - 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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College
algebra contents |
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