Using Geogebra to Verify if a function is odd, even or neither

In a PreCalculus or Calculus class, students often struggle to see how the definition of an even or odd function fits the mathematical definition.

To remind the student, a function is odd if it fits this definition:   f(-x)= -f(x)    Graphically, this means that for every point (x,y) belonging to the function,  then (-x, -y) is also a point on this same function.  This will appear in a graphing calculator as a function with point symmetry about the origin.  The first quadrant will map to the third quadrant; the second quadrant to the fourth - and the curve will be inverted.


A function is even if it fits the definition:  f(-x) = f(x)   This means that the y value associated with each distinct x is the same y value for the opposite of x.   This will appear in a graphing calculator as a function that is symmetrical to the y axis as  -x has the same height (y) as x does.

For the past 6 years, I have been using Geogebra to illustrate complex mathematical topics.  Here are some screenshots from a demonstration that the function   f(x)=x^4+x^2  is an even function and not an odd function.     g(x)=-f(x)  and h(x)=f(-x)

In the screenshot below you can visually see the f(-x)  *shown in red  does not equal  -f(x)  so it is NOT odd.

In this screenshot below you can visually see that  f(-x) = f(x) since the two graphs are superimposed and the conclusion is this function is even.