



LIST OF ALGEBRA LESSONS

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POINTS ON THE COORDINATE PLANE 
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The Concept of Point Coordinates


Points on a Number Line. The Concept of a Signed Distance


A Coordinate Line and a Coordinate System


Points on the xAxis


Points on the yAxis


The Coordinates of Points in the First Quadrant


The Coordinates of Points in Any Quadrant


A Distance between Two Points and a Midpoint


The Distance of a Point from the Origin


The Distance Between Two Points


The Midpoint of a Segment


The Distance Between Two Points in Different Axes Systems 

Transormations of Points and their Coordinates


Reflection of Points


Translation of Points


The Proportion in Points Coordinates


Different Dependencies Between the Points' Coordinates 



LINEAR FUNCTION 

General


Points on the Horizontal Line. Points on the Vertical Line


The Equation of the Vertical Axis 

The Equation of the Horizontal Axis


The Properties of a Point on a Line 

The Distortion of the Scales 

The Concept of a Slope


The Slope of a Segment between Two Points in the First Quadrant 

The Slope of any Segment between Two Points


The Slope of a Linear Function Graph y = mx


A Linear Function Passing through the Origin y = mx as a Graphic Representation of a Linear Proportion


The SlopeIntercept Form of Linear Equation y = mx + b


The Slope of a Linear Function Graph y = mx + b


The Meaning of the Free Term b in the Linear Function y = mx + b (Part I)


The Meaning of the Free Term b in the Linear Function
y = mx + b (Part II)


Proportion Properties of a Linear Function Not Passing through the Origin y = mx + b


The Representation of the xIntercept Point in a Linear Function in the Form y = mx + b


The Graphical Representation of the Moving Problems 

Parallel and Perpendicular Lines


The Equations of Parallel Lines


The Equations of Perpendicular Lines


A Perpendicular to a Line Passing through the Given External Point


The Distance from a Point to a Line


Standard Linear Equation Ax + By = C


Standard Linear Equation Ax + By + C = 0  General 

Standard Linear Equation Ax + By = C when A = 0 

Standard Linear Equation Ax + By = C when B = 0 

Standard Linear Equation Ax + By = C  Exploring the Slope 

Standard Linear Equation Ax + By = C  Exploring the yIntercept 

The Standard Equations of Parallel Lines 

The Standard Equations of Perpendicular Lines 

The Equivalent Standard Equations 

Other Forms of Linear Equation


The Equation of a Line of a Given Slope Passing through a Given Point.
Part I  General


The Equation of a Line of a Given Slope Passing through a Given Point.
Part II  The Pencil of Lines


A Family of Linear Functions Passing through a Given Point


The Linear Function Passing through Two Given Points


The Equation of a Segment 

The Intersection of Two Straight Lines


The Intersection Point of Two Lines


The Intersection Point of Many Lines. The Pencil of Lines


The Graphical Solution of Two Standard Linear Equations 

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QUADRATIC FUNCTION 

General


The Quadratic Function's Graph and Its Properties


The Vertex (Completed Square) Form of a Quadratic Function


The corresponding values of x
for a given value of y . Part I: The Family of Functions
y = x^{2} + c 

The
corresponding values of x for a given value of
y . Part II: The Family of Functions y = x^{2} + Bx +
C 

Solving Quadratic Equations 

Transformations of the Quadratic Function Graph


Horizontal Translation


Vertical Translation


Combined Translation 

Shrinking and Stretching


A Family of Quadratic Functions with the Vertex at the Given Point


The Factored Form of a Quadratic Function


The Meaning of the Factored Form of a Quadratic Function and Its
Graphical Representation 

The Quadratic Function as a Product of Two Linear Functions  Part I 

The Quadratic Function as a Product of Two Linear Functions  Part
II 

Exploring Parameters in Different Families of Quadratic Functions


Exploring Parameter B in the Family of Functions
y = x^{2} + Bx


Exploring Parameter k in the Family of Quadratic Functions y =
k(x^{2} + px + q)


Exploring Parameter A in the Family of Quadratic Functions y =
Ax^{2} + Bx + C


Exploring Parameter C in the Family of Quadratic Functions y = Ax^{2} + Bx +
C


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OTHER
FUNCTIONS 

Power and Polynomial Functions


Power Function


Polynomial Function  General


Different Third Degree Polynomial
Functions and their Graphs


Different Forth Degree Polynomial Functions and their Graphs


Exploring Parameter a in Function f(x) = (x  5)(x  a)(x + 3) 

Extrema of Third Degree Polynomial Function


Extrema and xIntercept Points of Fourth Degree Polynomial Function


Rational Functions  Introduction


Types of Rational Functions


Exponential and Logarithmic Functions


Introduction


The Family of Exponential Functions y = a^{x}


The Mathematical Constant e and its Meaning 

Two Families of Functions: y = e^{ax} and y =
ke^{x}


Logarithmic Function


Exploring the Properties of Function e^{x}


Examples of Exponential Growth


Absolute Value and Integer Functions


Absolute Value Function


Integer Function


Discrete Variable Functions


Function of Discrete Variable


Sequence and Sum


Inverse Functions


Square Power and Square Root Functions


Cube Power and Cube Root Functions


Exponential and Logarithmic Functions


Sine and Arcsine Functions


Inequalities and Linear Programming


Inequalities in One Variable


Inequalities in Two Variables


Inequalities of Functions


Solving a Problem of Linear Programming


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EXPLORING FUNCTIONS 

Functions Evaluation


The Necessity of a Unique Name for a
Function


The Use of a Function Name for Evaluating Functions


The Use of Existing Function Name for
Defining New Function


xIntercept, Extrema and Inflection Points


The Meaning of the xIntercept Point


The Sign of a Function


The Point of Maximum


A Steepness and Tangent Slopes in the Vicinity of the Maximum Point


The Point of Minimum


A Steepness and Tangent Slopes in the Vicinity of the Minimum Point


Increasing Function


Different Combinations of Positive /
Negative and Increasing / Decreasing Regions of a Function


Local and Global Extrema


Inflection Point  Introduction


General Rules of Functions' Graphs


Translation


Horizontal Translation


Examples of Horizontal Translation


Vertical Translation


Examples of Vertical Translation


Combined Translation


Examples of Combined Translation


The
Translation of Function Graph  Summary


A Pencil of Straight Lines


The Locus of Vertex Points of a Translated Quadratic Function


The Translation of an
Exponential Function's Graph


The
Translation of a Circle


Reflection


The Reflection of Points over the Axes 

The Reflection of Points through the
Origin 

The Reflection of Points  Summary 

The Meaning of the Reflection of a Function Graph


The Reflection of an Even Function Graph


The Reflection of an Odd Function Graph 

Reflection of Function Graph  Summary


Additional Examples of Reflection


Shrinking/Stretching


Quadratic Function's Graph


Exponential Function's Graph


The sine Function's Graph


Shrinking/Stretching of Function Graph  Summary


Applications


Reflection of Figures


Finding a Polynomial Function


Drawing a sine Function's Graph


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Discontinuity of Functions


Types of Discontinuity


Exploring Rational Functions


More Examples of Rational Functions


Trigonometric Functions


Operations with Functions


Two Linear Functions 

Addition & Subtraction


Multiplication


Division


Square Root of Product


Linear and Quadratic Functions


Addition & Subtraction


Multiplication


Division


Square Root of Product


Two Trigonometric Functions


Addition & Subtraction


Other Operations


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