2. 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/
4. 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
5. 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
6. How to Graph a Function
In the input line, enter the functional notation:
After doing so, press Enter and the graph will appear.
7. 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]
9. 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.
10. Example
• Graph:
2
2 -7 < x -1
( ) 1 -1 < x < 2
1
5 2 x 6
2
f x x
x
− ≤
= −
− + ≤ ≤
11. 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,
12. 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
Open Piecewise.ggb
Note: Geogebra has a built in command for graphing two functions given a specific condition. This is done using the IF command. This can be found in the HELP.
Also show Exam1.ggb
Use the Piecewise.ggb example.
Color, size, style, name, value, shape
Open Polynomial.ggb
Modify Axis: Click on MOVE and drag on axis to change scale.
To find function value: f( #)
To factor: Use Factor [f] . However if it is unfactorable it will return the original function.
To find X-int: Use Root command Root [f] or Use Intercept Two Objects Button
To find Y-int: Use Intercept Two Objects Button (Click on both)
To find max & min use the Extremum command. Extremum[f]
Also talk about the relationship between zeros and multiplicity, End behavior