Calculus - I
Calculus Contents A

Function definition, notation and terminology
Domain, range and codomain
Evaluating a function
Composition of functions (a function of a function)
Inverse function
Function's 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's 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

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
The graphs of the source cubic functions
The graphs of the translated cubic functions
The graphs of the quartic function
The graphs of the quartic functions types 1 and 2
The graphs of the quartic functions types 3/1 and 3/2
The graphs of the quartic functions types  4/1 . . . 4/6
Sigma notation of the polynomial
Coefficients of the source polynomial in the form of a recursive formula
Coefficients of the source polynomial function are related to its derivative at x0
Translated power function
Translated sextic function example
Graphs of rational functions
Basic properties of rational functions
Vertical asymptotes of rational functions
Horizontal asymptote of rational functions
The oblique or slant asymptote of rational functions
reciprocal function, equilateral or rectangular hyperbola
Translation of the reciprocal function, linear rational function
Graphs of rational functions examples
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