## Wednesday, July 2, 2014

### Geogebra Series II: Transforming a Graph With Sliders

One of the most powerful features of Geogebra is the slider.  Watch the video below to see how sliders can make your graphs dynamic.

You can use the above tool for presentation in your classes, or you can open a new Geogebra file and follow the steps below to create your own presentation.

The first step is to add a slider to the graphics view.  Click in the top left or right of the graphics view to keep the slider out of the way of the graph that you will add later.

Use -5 to 5 or -10 to 10 for the minimum and maximum values.  Now add sliders b, c, and d.

Choose your favorite function type, such as quadratics.  I can graph as many quadratic functions as I want by typing each function into the input bar at the bottom of the screen.  Or I can type one quadratic function into the input bar that can be transformed into any quadratic function (okay not all of them, just the ones with parameters between -5 and 5, or whatever you chose for your min and max values).

Use parameter b for horizontal stretch shrink.

Or for growth and decay

Hit enter, and prepare to be amazed!  Drag each of your sliders to see how the function is transformed.

You can use this parent graph tool, which includes many types of functions. Once students see functions being transformed dynamically, the conversations and types of questions we can ask get richer.

If students know the form of the function (y=a(x-c)^2+d in this case), they can discuss the similarities and differences between the parabolas in the family above.  They can notice that all of the parabolas have a vertex at (-2,-1), and an axis of symmetry at x=-2, and that there is a relationship between these values and the parameters c and d.  This is a good opportunity to practice vocabulary, and also to help students start understanding the difference between a parameter and a variable.  They can even use the parent graph tool to create their own graph family.

y=a*sin(b(x-c))+d

For the graphs above students might notice that the amplitudes are different and that a is between -5 and 0. For the graphs below they can recognize exponential growth (b>1), horizontal shifting (c varies), and maybe guess that the horizontal asymptote is y=0 (so d=0).

y=a*b^(x-c)+d

Once students have explored function transformations we can introduce other types of questions.   One example is to graph a parent function and transformed function and ask students to make generalizations on the parameters.  One of my favorite tricks is to take the numbers off of the axes so I can also ask them to write a possible function for the transformed graph.

If students know the form of the parent graph is y=a*abs(x-c)+d, they can reason that a<0, absolute value of a is less than 1, c<0, and d<0.

And of course there is the classic matching activity.

Links you may find useful:

Geogebra Tools from Making Math Visual blog.
Geogebra Wiki.  Includes tutorials on how to get started with Geogebra.