This interactive figure demonstrates the limit of [math]f(x)[/math] as [math]x\to\pm\infty[/math]. Drag the [color=#ff0000]red point[/color] on the [i][math]x[/math][/i]-axis to the right or the left to simulate [math]x\to\pm\infty[/math]. You can use the slider to select different example functions, or you can enter your own (the viewing window will reset when [math]f\left(x\right)[/math] is changed). You can change the maximum values on the [i][math]x[/math][/i]-axis with the[color=#0000ff] blue button[/color]. You can see the [color=#38761d]green point[/color] on the function and determine what value the function seems to be approaching or you can use the [color=#38761d]function value[/color] given in the right side of the figure. You can move the [color=#9900ff]purple point[/color] on the [math]y[/math]-axis (or enter a [math]y[/math]-value directly) to try to locate the horizontal asymptote. Not every function will have a horizontal asymptote and some may have two.

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