This applet illustrates the relation between the independent variable [math](x)[/math] and the dependent variable [math](y)[/math] for functions.[br][br]The drop down list allows you to chose a function to explore. The last function can be edited in the box that appears.[br][br]You can move the dot on the [math]x[/math] axis to change the [math]x[/math] value. The output [math]y[/math] value is shown along with arrows indicating the flow of information.[br][br]The middle mouse or shift mouse allows you to move the graph. The mouse wheel scales the graph. You scale the axes independently with the middle mouse over the axis.

Choose a function from the dropdown box. Choosing the last function in the list will allow you to enter your own function in the entry box. You can use some of the suggestions.[br][br]Are there [math]x[/math] values where the [math]y[/math] value is undefined or does not exist?[br][br]Are there [math]y[/math] values you cannot get with any [math]x[/math] value?[br][br]Are there more than one[math]y[/math] values for any [math]x[/math] values?[br][br]Why is the [math]x[/math] value called the independent variable?[br][br]If the [math]y[/math] value is undefined, then the corresponding [math]x[/math] value cannot be in the [u]domain[/u] of the function.[br]If a [math]y[/math] value cannot be obtained with any [math]x[/math] value ( in the domain ) it is not in the [u]range[/u] of the function.