A vertical asymptote is a line that a function approaches but never reaches.

The intersection of this line with the graph of y = f(x) can happen in one or more places. Whenever there are two vertical asymptotes, they will intersect at an oblique angle. So if the vertical asymptote is y = x, then there will be an intersection at 𝑥=0.

Similarly, if the vertical asymptote is y = √x, then 𝑥=√−12 and a portion of the graph will intersect it.

Additionally, for any function f(x) with two different values that feed into each other in such a way that one creates horizontal segments on either side of another

(as shown to the left), those lines are also considered asymptotes because they limit where this line can go. Discussion: In general, you need to make sure that when drawing graphs or solving equations you identify whether or not your final answer might


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