Construction of Inverse Function
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User Guide
Construction of Inverse Line
GeoGebra Applet: Inv_Straight_Line.ggb
Link: http://geogebrawiki.wikispaces.com/Inverse+function+-+Straight+line
GeoGebra tools:

Insert text: Creates static and dynamic text or LaTeX formulas in the Graphics
View.

Move: Drag and drop free objects with the mouse.

Slider: Creates a slider for a number or an angle.

Point: Creates new point in the drawing pad in the Graphics window.
GeoGebra commands:

1.
Reflect[ Object,Line]: Reflects Object about Line.
Create slider to make drawing of different lines in the Graphics window step by step as they are
constructed. Click on the
Slider tool and then in Graphics window. A dialog window opens
(Fig.1). GeoGebra suggests a for name of the slider (you can choose another name). Insert 1 for
min, 5 for max and 1 for Increment. Now slider can get value that is one of the numbers from 1
to 5. Moving the point on the slider will cause drawing of different lines one by one in order to
give better visualization of the concept function – inverse function (this will be set later in the
construction).
Fig.1
Click on the Slider tab and choose Vertical to make the slider position vertical in the Graphics
window (default option is horizontal). Uncheck the button
to make the slider moveable
on the screen.
Click on the Animation tab to change the speed of moving the point on the slider (default is 1)
and the way of moving the point on the slider (Oscillating, Increasing, Decreasing and
Increrasing (Once)). Choose Oscillating to move the point on the slider up and down.
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Construction of Inverse Function
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2.
Insert text Show line, Show Line y=x, Show reflected line, Check inversity (slide point A),
change the color of each of them and put them next to the slider a (Fig.2).
Fig.2
3.
Now draw the line y=3x+4.
Insert y=3x+4 in the Input bar in the down left bottom of the GeoGebra window and press the
Enter key. The line is drawn in Graphics window and equation of the line is written in the
Algebra window (Fig.3). GeoGebra names line c:y=3x+4. To change the look of the line right
click on the equation of the line in the Algebra window or line in the Graphics window and
choose Options. Click on the Color tab to change the color and the Style tab to change style and
thickness of the line.
4.
Type y=x in the Input bar to draw the line of the reflection. The line is drawn in the GeoGebra
window. Look in the Algebra window. GeoGebra names the line b:y=x. (a is already reserved
for the the name of the slider).
5.
Use command Reflect[ <Object>, <Line>] to reflect Object about Line.
Start typing d=Reflect[c,b] in the Input bar to reflect the line c:y=3x+4 about line of
reflection b:y=x. If GeoGebra suggests the desired command, hit the Enter key in order to place
the cursor within the brackets. If the suggested command is not the one you wanted to enter, just
keep typing until the suggestion matches.
The reflected line is drawn in the Graphics Window and equation of the line d:y=0.33x-1.33 is
written in the Algebra window (Fig.4).
Fig.3
6.
Now, mark points to check inversity. Click on the
mark point A.
Fig.4
Point tool and on the line c:y=3x+4 to
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Construction of Inverse Function
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Type B= (y(A), x(A)) in the Input bar, where y(A) means y coordinate of point A, and x(A)
means x coordinate of point A and press the Enter key. See that pont B lies on the line d (Fig.5).
Moving the point A through the line c indicates moving of the point B through the line d. That
means that if A(x,y) is a point that lies on the line c, there is only one point B(y,x) that lies on
the line d.
Fig.5
7.
Now make the drawing of the constructed lines dependent of a condition fulfilled. This allows
drawing of the lines step by step by moving the point on the slider down and up.
Right click on the line c:y=3x+4 in the Algebra or Graphics window and choose
Object
Properties. Click on the Advanced tab and type a<5 in Condition to Show Object. The line
c:y=3x+4 will be drawn in the Graphics window everytime the value of the slider a is smaller
then 5.
Repeat the procedure to make conditional appeareance of the line b (insert a<4), the line d (insert
a<3) and the points A and B (insert a=1).
8.
Testing the construction:
Move the point on the slider down or up to make drawing of the lines one by one.
Move the point A check inversity.
9.
View construction protocol:
From the View menu choose Construction protocol to view protocol of the construction
(Fig.6).
Fig.6
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