Vertical Asymptote

What is Vertical Asymptote?

A vertical asymptote of a tangent graph is a vertical line at an x-value where the function is undefined, and towards which the curve rises or falls without limit while never reaching or crossing it. For y = a tan bx + c the asymptotes occur where the angle bx equals ninety degrees plus any multiple of one hundred and eighty degrees, which in radians is pi over two plus any multiple of pi, so they are spaced exactly one period apart. Each asymptote separates the graph into an independent branch, and a correct sketch never joins one branch to the next.

This definition is part of the Trigonometry chapter in Cambridge O Level Additional Mathematics.

Concepts related to Vertical Asymptote

• undefined values
• period
• separate branches
• unbounded function