Unit G Summary Question #4: Vertical Asymptotes and Holes

What is the difference between a graph having a vertical asymptote and a graph having a hole?

A graph that has a vertical asymptote means that a function can approach but never touch that vertical asymptote. A graph that has a hole means that a function will get close to it, skip it, and continue on as if it were there but you actually do not touch it. The image on the left shows a vertical asymptote as a red dashed line.The image on the right shows a few holes in the functions. The every unusual function with a numerator and denominator will have a vertical asymptote whereas a hole only exists if something cancels when factoring the function.