When analyzing rational functions, some of the main characteristics include domain, range, asymptotes, and points of discontinuity. A related skill is determining the equation given a graph. Another lesson specifically about points of discontinuity can be found at:

https://mathpqjq.com/point-of-discontinuity/

For more information related to the end behavior of rational functions, you can watch the video at:

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:end-behavior-of-rational-functions/v/end-behavior-of-rational-functions