In this environment you can explore this behavior for linear, quadratic and cubic polynomials,
as well as for exponential and absolute value functions.
Any of these functions can be seen as a combination of even and odd functions.
You can enter a polynomial of your choice by dragging “rings” around the screen.
The environment will display the even and odd functions that can be combined to make your function.
In the case of exponential functions you can drag a ring to fix the intercept of the function with the y axis
and adjust a slider to fix the growth or decay of the exponential.
In the case of absolute value functions, you can drag a ring to position the vertex
and use a slider to fix the slope of the sides.
Conjecture what the relationship between the three functions f(x), g(x),k(x)
What characterizes each of the functions: is it odd, even, not odd and not even?
The original applet was taken from http://tube.geogebra.org/student/m284367