VISUAL-DYNAMIC SCHOOL MATHEMATICS LESSONS

VISUAL-DYNAMIC ALGEBRA

POINTS ON THE COORDINATE PLANE

Points on the x-Axis

Points on the y-Axis

The Coordinates of Points in the First Quadrant

The Coordinates of Points in Any Quadrant

Different Dependencies Between the Points' Coordinates

Reflection of Points

The Distance Between Two Points in Different Axes Systems

The Midpoint of a Segment

LINEAR FUNCTION

A Family of Linear Functions Passing through the Origin

The Equation of the Horizontal Axis

The Equation of the Vertical Axis

A Family of Linear Functions y = ax + b

A Family of Parallel Linear Functions

A Family of Perpendicular Linear Functions

A Linear Function Passing through Two Given Points

A Linear Function Passing through a Given Point with a Given Slope

A Family of Linear Functions Passing through a Given Point

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QUADRATIC FUNCTION

The Quadratic Function's Graph and Its Properties

The Completed Square Form of a Quadratic Function

Horizontal Translation

Vertical Translation

Combined Translation

Shrinking and Stretching

Solving Quadratic Equations

The Quadratic Function as a Multiplication of Two Linear Functions

A Family of Quadratic Functions   y = x² + bx

Exploring Parameter a in the Family of Quadratic Functions   y = a(x² + bx + c)

Exploring Parameter a in the Family of Quadratic Functions   y = ax² + bx + c

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MORE FUNCTIONS

Power and Polynomial Functions

Power Function

Polynomial Function - General

Graph of Third Degree Polynomial Function

Graph of Fourth Degree Polynomial Function

x-Intercept Points of Third Degree Polynomial Function

Extrema of Third Degree Polynomial Function

Extrema and x-Intercept Points of Fourth Degree Function

Rational Functions - Introduction

Types of Rational Functions

Exponential and Logarithmic Functions

Introduction

Exponential Function

Logarithmic Function

Exploring the 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

How to Use a Function Name

x-Intercept, Extrema and Inflection Points

X-Intercept Points

The Sign of a Function

The Extrema of a Function

Increasing Function

The Local and Global Extrema

Inflection Point - Introduction

General Rules of Functions' Graphs

Translation

Horizontal Translation

Vertical Translation

Combined Translation

A Pencil of Straight Lines

The Locus of Vertex Points

Exponential Function's Graph

Translation of Circle

Reflection

Reflection of Points

Quadratic Function's Graph

Additional Examples

Shrinking/Stretching

Quadratic Function's Graph

Exponential Function's Graph

The sine Function's Graph

Applications

Reflection of Figures

Finding a Polynomial Function

Drawing a sine Function's Graph

Discontinuity of Functions

Types of Discontinuity

Exploring Rational Functions

More Examples of Rational Functions

Trigonometric Functions

Operations with Functions

Two Linear Functions

Linear and Quadratic Functions

Two Trigonometric Functions

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VISUAL-DYNAMIC TRIGONOMETRY

Basic Trigonometric Functions

The sine Function

The cosine Function

The Tangent Function

The Tangent Function as a Ratio sine/cosine

Inverse Trigonometric Functions

General

Exploring the arcsine Function

Operations with Trigonometric Functions

The Function  f(x) = sinx + cosx  and its Graph

The Function  f(x)= sin²x + cos²x  and its Graph

The Absolute Value of Basic Trigonometric Functions

Transformations of the sine Function

Changing the Amplitude

Changing the Period

Horizontal Translation

Combinations with Trigonometric Functions

Analyzing Function  f(x) = x + sinx  and its Graph

Analyzing Function  f(x) = x² + sinx  and its Graph

Analyzing Function  f(x) = xsinx  and its Graph

Analyzing Function  f(x) = x²sinx  and its Graph

Analyzing Function  f(x) = (sinx)/x  and its Graph

Analyzing Function  f(x) = sin(1/x)  and its Graph

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VISUAL-DYNAMIC CALCULUS

Derivatives

The Linear Approximation of a Function

A Tangent as a Limit of a Chord Between Two Points on a Graph

Investigation of an Argument Increment D x

Representing a Function Graph by Unit-Length Tangents

Investigating the Derivative of Power Function using the (x,Slope) Points

The Geometric Properties of the Tangent of Parabola y = x²

The Geometric Properties of the Tangent of Parabola y = ax²

The Geometric Properties of the Tangent of any Parabola

The Graph of the Derivative of a Function

The First and the Second Derivatives of a Function

Integrals

The Geometrical Meaning of the Integral of f(x) = x

The Geometrical Meaning of the Integral of f(x) = x²

The Geometrical Meaning of the Integral of Square Root of x

The Geometrical Meaning of the Integral between Two Points on a Graph

The Graph of an Antiderivative and the Constant of Integration

The Numerical Integration and the Definite Integral Function

The Concept of Signed Area

The Area Between Two Graphs - Part I

The Area Between Two Graphs - Part II

The Function of the Integral and its Derivative

The Normal Distribution

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