[list][*]Use the input box for [math]f(x)[/math] to input a function formula. Use the input boxes for [math]a[/math] and [math]b[/math] to set the endpoints of the domain of [math]f(x)[/math]. This just helps to narrow down some calculations that the computer will have to do in this application. [/*][*]Use the checkbox for "Evaluate" or "Solve" one at a time to see the process for evaluating or solving a function, respectively. [/*][*][b]Evaluate: [/b]Use the slider tool for [math]c[/math] to adjust the input value. Think of [math]c[/math] as a constant [math]x[/math]-value that we are free to choose. Then use the unlabeled black slider tool to observe the visualization for evaluating a function. When you want to switch to "Solve," uncheck the checkbox for Evaluate to keep the graph from becoming too cluttered. [/*][*][b]Solve:[/b] Use the slider tool for [math]y_0[/math] to adjust the output value. Think of [math]y_0[/math] as a constant [math]y[/math]-value that we are free to choose. Then use the unlabeled black slider tool to observe the visualization for solving a function. When you want to switch to "Evaluate," uncheck the checkbox for Solve to keep the graph from becoming too cluttered. [/*][/list]

A [b]function [/b]is a set of ordered pairs [math](x,y)[/math] that satisfies a special condition: each x value can only be paired with one y-value. (This condition is often visualized with the [i]Vertical Line Test[/i].) This condition allows us to think of a function as an [b]input-output relationship[/b]. When you plug in an input (x), you can only get one output (y). This input-output relationship is expressed as:[br][br][math]f(x)=y[/math][br][br]which is read as "f of x equals y." The input [math]x[/math] is called the [i]independent variable[/i], and the output [math]y[/math] is called the [i]dependent variable[/i]. Typically the quantity represented by [math]y[/math] somehow depends on the quantity represented by [math]x[/math]. This means we can think of it like a change in the value of [math]x[/math] [i]causes [/i]a change in the value of [math]y[/math]. [br]