How to (2): Functions, Dynamic Text and Graphics 2

GeoGebra Institute of MEI, Oct 29, 2015

Table of Contents

  1. Introduction
    1. Introduction to functions, dynamic text and Graphics 2
  2. Examples
    1. Quadratic inequalities
    2. The unit circle and the graphs of sin, cos & tan
    3. Invariant lines of matrix transformations
  3. Skills
    1. Functions
    2. Advanced Dynamic Text
    3. Graphics 2
  4. Constructions
    1. Construction 1: Differentiation from 1st principles
    2. Construction 2: Gradient function
  5. Tasks
    1. Tasks

1.

Introduction

  • 1. Introduction to functions, dynamic text and Graphics 2

1.1.

Introduction to functions, dynamic text and Graphics 2

In this lesson you will be introduced to how GeoGebra handles functions, formatting of dynamic text and using the Graphics 2 view.[br][br]Some examples of GeoGebra files are displayed in section 2 to give you a sense of what can be achieved.  You should then work through the skills and constructions section before trying the tasks.
– GeoGebra Institute of MEI

2.

Examples

The examples feature the use of functions, properly formatted dynamic text and the Graphics 2 screen.

  • 1. Quadratic inequalities
  • 2. The unit circle and the graphs of sin, cos & tan
  • 3. Invariant lines of matrix transformations

2.1.

Quadratic inequalities

Drag the points A and B to vary the quadratic
Quadratic inequalities
– GeoGebra Institute of MEI

2.2.

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2.3.

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3.

Skills

  • 1. Functions
  • 2. Advanced Dynamic Text
  • 3. Graphics 2

3.1.

Functions

Adding functions
[list][*]GeoGebra will graph all equations except conic sections (lines, parabolas, circles, ellipses and hyperbolas) as functions[br][br][/*][*]Lines, parabolas and hyperbolas can be entered as Cartesian equations or functions[br][br][/*][*]Equations such as y=x^3 or y=sin(x) will automatically be converted to functions[br][/*][/list][br]Try entering some equations and functions in the input bar.
– GeoGebra Institute of MEI

3.2.

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3.3.

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4.

Constructions

  • 1. Construction 1: Differentiation from 1st principles
  • 2. Construction 2: Gradient function

4.1.

Construction 1: Differentiation from 1st principles

Construction steps
[list=1][*]In the input bar type [b]f(x)=x^2[/b] and press enter.[br][br][/*][*]Add a [b]New Point[/b], A,on the curve[br][br][/*][*]In the input bar set [b]a=x(A)[/b][br][br][/*][*]Add a [b]Slider[/b]: Name: h,  Min: 0, Max 1, Increment 0.01.[br][br][/*][*]In the input bar add the point [b](a+h, f(a+h))[/b][br][br][/*][*]Add the [b]Line[/b] through A and B[br][br][/*][*]In the input bar set [b]H=f(a+h)-f(a)[/b][br][br][/*][*]In the input bar set [b]q=H/h[/b][br][br][/*][*]Create a [b]Text box[br][/b]- switch LaTeX formula on[br]- in the Advanced tab select the fraction a/b[br]- replace a and b with H and h from the GeoGebra objects menu [br]- type [b]=[/b] [br]- select q from the GeoGebra objects menu[br][/*][/list]
– GeoGebra Institute of MEI

4.2.

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5.

Tasks

  • 1. Tasks

5.1.

Tasks

Create GeoGebra worksheets that feature the use of function, advanced dynamic text and Graphics 2.[br][br]Suggested ideas:[br][list][*]The graph of the unit circle and trig functions for degrees/radians.[/*][*]The graph of the a function and its derivative.[/*][*]The graph of a function and its integral.[/*][*]Graphs of composite functions.[/*][/list]
– GeoGebra Institute of MEI

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