垂直渐近线

A vertical asymptote is when a function goes up so quickly, it's almost as if it is vertical. (Exponential is not vertical, just for clarification).

Consider the graph of $y=\frac{1}{x}$.

As you can see from the graph above, it is a hyperbola. As x approaches 0 from the right side, the function shoots up to infinity. As x approaches 0 from the left side, f drops to negative infinity.

An important thing to know is that **vertical asymptotes are never crossed **.

For example, the function $y=\frac{1}{x}$ has a vertical asymptote at $x=0$, but there is no value of the function at x=0 (it is undefined.) In general, vertical asymptotes occur when functions are undefined.

Problems 1-6 on the following worksheet are good practice for the skill you just learned:

http://www.dsisd.txed.net/DocumentCenter/View/59360

(Video) Finding Vertical Asymptotes of Rational Functions

by PatrickJMT

Here's a video by patrickJMT showing you how to find the asymptote of a rational function.