# Algebra and Functions

In this tutorial we cover graphing functions and equations.  We'll use check boxes and sliders, and we'll add text to a worksheet.
The complete GeoGebra file is here: Tutorial-2.ggb.

 Open a new, blank worksheet.  Right-click anywhere on the graphics view and select "Drawing Pad..." Here you can find options for showing and hiding axes and the grid as well as many other axes/grid options.  Choose some settings you like. In the Input Bar at the bottom of the screen, type a function.  I typed f(x) = sin(5x) + (1/3)x^2 + 1.  GeoGebra understands standard calculator syntax. Now you can use f(x) to create other functions.  In the Input Bar type, for example, g(x) = f(x) - 2. In the Input Bar, use the up and down arrows to scroll through your previous entries.  See what happens when you click and drag the graph of  f(x). GeoGebra can also graph linear and quadratic equations.  Try typing  x^2 + 2y^2 = 16.  Unfortunately, GeoGebra cannot graph equations of degree 3 or higher. To redefine an object, you can double-click it in the algebra view.  A better way is to Alt-click an object to make its definition appear in the input bar - then you can type changes to its definition. We'll make some check boxes to show and hide our graphs. Find the Check Box tool .  Click somewhere on the screen.  A dialogue box appears asking for caption; type "functions".  From the drop down menu, select the functions  f  and  g  you have previously defined, then hit the Apply button. Now you have a check box to show and hide the functions.  You can create a similar check box to show and hide the ellipse. Now we'll see how sliders are used. Find the Slider tool  then click somewhere on the screen.  Name your slider  m  and accept the other defaults.  Make another slider the same way, but name it  n.  Alt-click on your function g(x) to make its definition appear in the Input Bar and redefine it as     g(x) = f(m x) + n Note that you need a space between m and x to indicate multiplication. Observe the effect of moving the sliders. Let's add some text. Find the Text tool and click somewhere on the screen.  Type  Transformations of Functions  and hit OK.  You can reposition the text somewhere suitable. Pan the screen around a little (Ctrl-click and drag the graphics view) and see how the text moves with the background.  To prevent this, you can right click on the text and choose "Absolute Position on Screen." Right-click on the text and choose Object Properties.  In the Text tab you can change its size and other properties. Select the Text tool again and click somewhere on the screen.  Type     "f(x) = " + f Text in quotes is literal, and we are concatenating it with the function f. Select the Text tool one last time and click somewhere on the screen.  Type     "g(x) = f(" + m + "x) + " + n Can you see how this produces the output on the right?

Final thoughts
• See how zooming in and out affects the view.  Good trick: Shift-click and drag an axis to scale only along that axis.  You can always right click and select "Standard View" to return back to normal.
• I often Alt-click on objects to inspect their definition in the Input Bar and make changes.
• The manipulation of boolean values can be effective and fun.  Try Ctrl-E to open the Object Properties dialogue box, select an object, then click the Advanced tab.  There is an input box titled "Condition to Show Object".  You can type in boolean values there, and even combine them by typing && (and), || (or) and ! (not).  When the value in the box is true the object is visible.  We'll see more of this in Tutorial 8 - Showing and Hiding Objects.
• When adding text, you can check the box next to "LaTeX formula".  This will allow you to use some basic LaTeX formatting.  For instance, x^2 will produce a true superscript.
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