Even and Odd Functions - I
- Judah L Schwartz
Even and Odd Functions An even function is one that is symmetric about the y axis. Such functions have the property that f(x) = f(-x). An odd function is one that is symmetric with respect to rotation by 180 degrees around the origin. Odd functions have the property that f(x) = - f(-x). 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. Challenge – Given a function, how can you calculate the even and odd functions that combine to make that function?