If a function value approaches [math]\pm\infty[/math] as [math]x[/math] approaches some value [math]c[/math], then there is a vertical asymptote at [math]x=c[/math]. By testing values of [math]x[/math] on either side of [math]c[/math], we can determine which direction the function is heading.

Enter a fucntion in the f(x) box. Drag the blue point on the x-axis to the location of the vertical asymptote. The two one-sided limits along with the overall limit are calculated and displayed. Now enter various test values of x to "approach" the vertical asymptote from one side or the other. Watch how the y-value changes as you get closer.