Notes

Parent guide with extra practice problems

As you can see in the examples above, asymptotes can be diagonal lines or even curves. However, in this course, asymptotes will almost always be horizontal or vertical lines. The graph of a function has a horizontal asymptote if, as you trace along the graph out to the left or right (that is, as you choose x‑coordinates farther and farther away from zero, either toward infinity or toward negative infinity), the distance between the graph of the function and the asymptote gets closer to zero.

A graph has a vertical asymptote if, as you choose x‑coordinates closer and closer to a certain value, from either the left or right (or both), the y‑coordinate gets farther away from zero, either toward infinity or toward negative infinity.