This applet is to explore odd and even functions. Recall that an even function has the property that [math]f\left(x\right)=f\left(-x\right)[/math] and an odd function has the property that [math]f\left(x\right)=-f\left(-x\right)[/math].[br][br]The example function shown here (in yellow) is [math]y=x^2[/math]. Is this an odd or even function? You can test this by clicking on the check box next to [math]f\left(-x\right)[/math] (try it). This will produce a red curve [math]y=f\left(-x\right)[/math]. Notice, that the red curve sits on top of the yellow curve. Hence [math]y=x^2[/math] is an even function. Now uncheck the middle check box and click on the bottom check box. This will produce a blue curve [math]y=-f\left(-x\right)[/math] that does not match the yellow curve.[br][br]Now try the function [math]y=x^3[/math]. 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 [math]y=x^3[/math] is odd or even.[br][br]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 [math]y=e^x[/math]). Note that many functions are neither odd nor even!!!