GeoGebraPrecalculus

Dr. Christine Brady and Vera Hu-HynemanSuffolk County Community College

What is GeoGebra?Dynamic mathematics software for all levels

of education that joins •Arithmetic•Geometry•Algebra •Calculus

The web address for GeoGebra is: http://www.geogebra.org/cms/

The page

Reference Websites

•Math 247  --tutorial for teachers

•Wiki --information about GeoGebra (it is written in java, so program is available for multiple platforms), use to learn geometry and more.

http://en.wikipedia.org/wiki/GeoGebra

Using Geogebra in Precalculus•Graphs and Properties of Functions

▫Symmetry▫Transformations

•Applications of Trigonometric Functions▫Law of Sines and Cosines

•Polar Graphs•Conics •Make graphs for tests

▫Visualize piece-wise functions

How to Graph a FunctionIn the input line, enter the functional notation:

After doing so, press Enter and the graph will appear.

Restricted Domain•To graph a function over the interval

[a,b], use the FUNCTION command.

•The syntax for the FUNCTION command is:▫Function[Function, a, b]

Piecewise-defined Functions

Graphing piecewise-defined functions

•Graph each piece separately over the indicated domain (x-values)

•Plug in the endpoints of the indicated domain for each piece to begin graphing▫If the endpoint is included then use a

closed circle▫If the endpoint is not included then use an

open circle.

Example

•Graph:

2

2 -7 < x -1

( ) 1 -1 < x < 21 5 2 x 62

f x x

x

How to Plot Points▫Use the Point Tool

This button is located on the toolbar.

To create a point, click on the above button and then the desired coordinates.

By default the point will be solid.

Characteristics of the point can be changed by going to Object Properties,

Properties of Polynomials•After graphing a polynomial function,

Geogebra has the ability to▫Factor the polynomial▫Find the following:

Function Value for a specific x-value Minimum Value Maximum Value X-intercepts Y-intercept

Symmetry

Transformations

Applications of Trig

Rational

Polar Graphs

Conics