Functions, Function definition notation and terminology, Domain and range of function, Evaluating functions, Composition of functions or function of function, Inverse function, Graph of function, Properties and characteristic points of graph of function, Roots of function, Zeros of function or x-intercepts of function, y-intercept of function, Increasing function, Decreasing function, Instantaneous rate of change of function, Derivative of function, Continuity and discontinuity of function, Vertical asymptotes, Horizontal asymptote, Slant or oblique asymptote, Stationary points of function, Critical points of function, Turning points of function, Extremes of function, maximums and minimums of function, Local maximums, local minimums of function, Points of inflection of function, Symmetry of function, Parity of function, Odd and even functions, Transformations of original or source function, Transformations of functions expression, How some changes of function's notation affect graph of function, Translations of graph of function, Reflections of graph of function, Types of functions, Basic classification of functions, Algebraic functions and transcendental functions, Polynomial functions, Rational functions, Reciprocal function, Transcendental functions, Exponential and logarithmic functions, Inverse functions, Trigonometric functions, Circular functions, Inverse trigonometric functions, Arc functions, Graphs of elementary functions, Graphs of algebraic functions, Graphs of transcendental functions, Graphs of polynomial functions, Graph of source polynomial, Translating graph of polynomial functions, Parallel shifting of graph of polynomial functions, Coordinates of translations and their role in polynomial expression, Graph of linear function, Graph of quadratic function, Graphs of cubic functions, Graphs of quartic functions, Graphs of translated power functions, Graphs of translated monomial functions, graphs of rational functions, basic properties of rational functions, Graph of reciprocal function, Graph of equilateral or rectangular hyperbola, Translation of reciprocal function, Linear rational function, Graphs of transcendental functions, Graphs of exponential and logarithmic functions, Graph of logarithmic function, Graph of exponential function, Graphs of trigonometric functions, Graphs of inverse trigonometric functions, Graphs of arc functions, graph of sine function, sinusoid, Graph of cosine function, Graph of arc-sine function, Graph of arc-cosine function, Graph of tangent function, Graph of cotangent function, Graph of arc-tangent function, Graph of arc-cotangent function, Graph of cosecant function, Graph of secant function, Graph of arc-cosecant function, Graph of arc-secant function

Pre-calculus Contents D

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

Pre-calculus Contents