Transformation of polynomial expression from general to source form, Transformation of polynomial expression from source to general form, Deriving coordinates of translation formulas of polynomial, Deriving coefficients of source polynomial function, Quadratic function formulas, Cubic function formulas, Quartic function formulas, Sigma notation of polynomial, Coefficients of source polynomial in form of recursive formula, Coefficients of source polynomial relate to its derivative, General or translated form of polynomial, Coordinates of translations of polynomial function, Coefficients of source polynomial formulas, Quintic polynomial formulas, Sextic polynomial formulas, Translated monomial or power function graphs, Roots of translated monomial function, Even and odd power functions, Translated sextic function example, Rational functions, Basic properties of rational functions, Graph of reciprocal function, Equilateral or rectangular hyperbola, Translation of reciprocal function, Linear rational function, Graphing rational functions, Vertical asymptotes of rational functions, Horizontal asymptotes of rational functions, Oblique or slant asymptotes of rational functions, Graphs of rational functions examples, Exponential and logarithmic functions and equations, Inverse functions, Translated logarithmic function, Translated exponential function, Rules and properties of logarithms, Natural and common logarithm relations, Natural to common logarithm conversion, Common to natural logarithm conversion, Changing the base of logarithms, Logarithmic identities, Exponential equations, Logarithmic equations, Trigonometric functions, Calculations of values of trigonometric functions, Trigonometric functions formulas, reference angles, Basic relationships between trigonometric functions of the same angle or arc, Addition formulas and related identities, Sum and difference formulas for trigonometric functions, Deriving addition formulas for sine and cosine functions, Addition formulas for tangent and cotangent functions, Trigonometric functions of double angles, Double angle formulas, Trigonometric functions expressed by half angle, Trigonometric functions of double angles expressed by tangent function, Trigonometric functions expressed by tangent of half angle, Half angle formulas, Trigonometric functions expressed by cosine of double angle, Sum to product and product to sum formulas or identities, Sum to product formulas for sine and cosine functions, Sum to product formulas for tangent and cotangent functions, Product to sum formulas for sine and cosine functions, Trigonometric identities examples

Pre-calculus Contents F

Transition of the polynomial expression from the general to source form and vice versa

Deriving the coordinates of translations formulas and the coefficients of the source polynomial function

Quadratic function

Cubic functions

Quartic functions

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

The general form or translatable form of the polynomial

The coordinates of translations and the coefficients of the source function formulas

Quadratic formulas

Cubic formulas

Quartic formulas

Quintic formulas

Sextic formulas

Translated monomial (or power) function

Translated monomial function graphs

Translated sextic function example

Rational Functions

Basic properties of rational functions

The graph of the reciprocal function f (x) = c/x, equilateral or rectangular hyperbola

Translation of the reciprocal function f (x) = (ax + b)/(cx + d), linear rational function

Graphing rational functions

Vertical asymptotes of rational functions

Horizontal asymptotes of rational functions

The oblique or slant asymptote of rational functions

Graphs of rational functions examples

Exponential and Logarithmic Functions and Equations

Inverse functions

Exponential functions

Logarithmic functions

Translated logarithmic and exponential functions

Rules and properties of logarithms

Natural logarithm and common logarithm conversions

Changing the base - different logarithmic identities

Exponential and logarithmic equations

Solving exponential and logarithmic equations

Exponential equations

Logarithmic equations

Trigonometric Functions

Calculation of values of trigonometric functions

Trigonometric reduction formulas - the reference angles

Calculation of values of trigonometric functions of an arbitrary angle x examples

Basic relationships between trigonometric functions of the same angle

Basic relationships between trigonometric functions of the same angle shown in the unit circle

Basic relationships between trigonometric functions of the same angle shown in the tabular form

Basic relationships between trigonometric functions of the same angle examples

The addition formulas and related identities

The sum and difference formulas for the trigonometric functions

Deriving the addition formulas for sine and cosine functions

The addition formulas for tangent and cotangent functions

Trigonometric functions of double angles, double angle formulas

Trigonometric functions expressed by the half angle

Trigonometric functions of double angles expressed by the tangent function

Trigonometric functions expressed by the tangent of the half angle

Half angle formulas

Trigonometric functions expressed by the cosine of the double angle

Sum to product and product to sum formulas or identities

Sum to product formulas for the sine and the cosine functions

Sum to product formulas for the tangent and the cotangent functions

The product to sum formulas for the sine and cosine functions

Trigonometric identities examples

Pre-calculus Contents