This interactive figure dynamically illustrates the meaning of the terms [i]domain [/i]and [i]range[/i] of a function in the setting where the function is displayed as a graph.[br][br]The [i]domain [/i]of a function is the set of all allowable input values ([math]x[/math]-values) for which the function is defined. (We say [math]a[/math] is in the domain of [math]f[/math] if [math]f(a)[/math] is a real number.)[br][br]The [i]range [/i]of a function is the set of all possible output values ([math]y[/math]-values) the function can produce. (We say [math]b[/math] is in the range of [math]f[/math] if there exists some number [math]a[/math] such that [math]f(a) = b[/math].)[br][br]Use this interactive figure to help you identify the domain and range of a function by inspecting its graph.

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]

Slide w to adjust the rectangle and observe the area.[br]What is the length and width of the 3 sided rectangle that maximizes the area?