This applet is to explore odd and even functions. Recall that an even function has the property that and an odd function has the property that .
The example function shown here (in yellow) is . Is this an odd or even function? You can test this by clicking on the check box next to (try it). This will produce a red curve . Notice, that the red curve sits on top of the yellow curve. Hence is an even function. Now uncheck the middle check box and click on the bottom check box. This will produce a blue curve that does not match the yellow curve.
Now try the function . To achieve this, type f(x)=x^3 into the input box at the bottom of the applet. Use the check boxes to see test whether is odd or even.
Try this with some examples of your own. You could try f(x)=cos(x), f(x)= sin(x) or f(x) = exp(x) (that is ). Note that many functions are neither odd nor even!!!