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GeoGebra Talk - A basic introduction
- 1. GeoGebra Precalculus Dr. Christine Brady and Vera Hu-Hyneman Suffolk County Community College
- 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/
- 3. The page
- 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
- 13. Symmetry
- 14. Transformations
- 16. Rational
- 17. Polar Graphs
- 18. Conics
Editor's Notes
- Functions – Linear, Quadratic, Polynomials, Exponential, Logarithms, Trigonometric, inverse functions, Properties – max, min, zeros, intercepts, domain, range, increasing, decreasing,
- Sample .ggb
- This can be used to graph piece-wise functions.
- 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