Vertical asymptote: Given by an equation such as x=c, and represented graphically by a vertical line. Graph does not touch this asymptote, but gets increasingly closer to it. Vertical asymptotes are associated primarily with functions defined as ratios. If such a function becomes undefined as x approaches some number c, then x = c is the equation of the vertical asymptote.
The vertical asymptote of the graph of y=1/x is x=0. The vert. asy. of the gr. of y = 5 / (x-1) is x=1. The vert. asy of the graph of y = sin x / cos x = tan x is x = pi/2 plus or minus n times pi: 3pi/2, 5pi/2, etc., because cos x = 0 at such values.
