MATH 6700
Independent Study

Using the GeoGebra software to plot the graphics of functions in College Algebra
The Minh Tran

Outline
Plot the graphics of quadratic and absolute function
Quadratic function
Absolute function

Plot the graphics of rational functions with vertical, horizontal, and slant asymptotes
a) Rational functions with vertical and horizontal asymptotes
b) Rational functions with vertical and slant asymptotes

3) Plot exponential and logarithmic functions.
a) Exponential function
b) Logarithmic function
c) The inverse characteristics of exponential and logarithmic functions


CONTENT
Plot the graphics of quadratic and absolute function
a) Quadratic function
First, we would plot the basic function by the following steps:
Step 1:
● Input the function f(x) = x^2 directly at the last row of your worksheet in GeoGebra. We would see the figure follows as:



● Type “Enter”, we have the graph of the basic function




Step 2:

By the applying of the formula: for the basic functionWe would plot a new graphic of the function which is compared to the basic function
Where
a = 1>0: The graphic of f(x) will open up
h = 3 > 0: The graphic of f(x) will be translated 3 units to the right
k = 3 > 0: The graphic of f(x) will be translated 3 units up.
Hence, the vertex A(0,0) of the graphic of f(x) would be translated to the vertex B(3,3).
● Input the function F(x) = (x-3)^2 + 3 at the last row of your worksheet and press “Enter”




,and then we can change the colors for the graphics by
● Click on each graph with your mouse directly, and
● Choose the colors at the tool as the figure below:




Now, we continue to get the two vertices A(0,0) and B(3,3) of the graph f(x) and F(x) by ● Choose the tool:


● Set the points at the vertex of each graphic.
We have the two graphics of f(x) and F(x) with two vertices in the Cartesian coordinate system, which is shown as the figure:





Finally, it is easy to see that the graphic of f(x) translated from the vertex A(0,0) to the vertex B(3,3) of the graphic of F(x).
Step 3:

As you know, we would use an effect of visual aid in the learning and teaching process with GeoGebra software. That is using of the slip of graphics by setting two parameters a and b. Generally, instead of the two vertices A(0,0) and B(3,3) by using the parameter a for abscissa x and the parameter b for ordinates y.
To do this, we choose the slider tool
● Choose the tool on the toolbar


● Set the two values a and b on the empty space of the coordinate system
● Double click on the symbol and continue to choose the values of min and max for a and b from 0 to 3 with the step is 0.5 at the Slider window




● At the Basic window, we choose the tools such as Show Object, Show Label, Animation On as the figure:



The figure below displayed the slip of the graphic of f(x) to the graphic of F(x)





b) Absolute function

Similarly, we also can plot the graphs of absolute function follows as:
From the graphic of the basic function f(x) = |x|, it will be translated to the graph of G(x) =|x+4|- 4 and F(x)=|x-2|+4 with the translations from the vertex A(0,0) to the vertices B(2,4) and C(-4,4). Thus, we have the following figure



As the graph of quadratic function above, we would show the slip of the graphic of f(x) to the graphic of G(x) and the slip of the point B from A(0,0) to C(-4,4).




2) Plot the graphics of rational functions with vertical, horizontal, and slant asymptotes
a) Rational functions with vertical and horizontal asymptotes

We would continue to plot the rational function with the vertical asymptote x = 3 and the horizontal asymptote y = 2 by the following steps:

Step 1:

● Input the function f(x) = (2x +4)/(x-3