by Algebra Xpressor, but it doesn't
make sense at all according to our analysis. . I could find out an interesting feature
from the graph with Algebra Xpressor. The function should have values no
matter what the sign of x is. And, the function 
should have the same
value for any two different x and -x. That means that the graph should be
symmetric by y-axis. Students can differentiate the function and they obtain
. For x=1, the function has y=1. The graph should pass through
the origin.
The following is the graph of by Algebra Xpressor, but it doesn't
make sense at all according to our analysis.
I thought that this could be a chanllenge for students to make a logical
conjecture about the graph of the function and complete the half of it.
The next is showing and .
If students really understood the relationship between a function and its differential function, then this kind of limitation from the mathematical application itself would be easily corrected and make an advanced learning experience for the students.