My students were having a lot of trouble with understanding all of the ideas that come along with graphing rational functions. So, I created this card sort that students can use to practice. Students are given a mat that contains a chart with 6 functions and columns for vertical asymptotes, holes, horizontal asymptotes, slant asymptotes, x-intercepts, and y-intercepts. They must also match the graphs that go with each function.
Students are given pieces that match to the places in the graph. I suggest laminating the small pieces. You may wish to laminate the mats and graphs as well. All of the pieces must be used, so this helps students organize this topic in their minds and to start to see patterns.
I have also included a quiz that I used with my class that is in a similar format. There is a “word bank” that lists all of the choices for the vertical asymptotes, horizontal asymptotes, slant asymptotes, x-intercepts, and y-intercepts. Students use the choices and then draw the graphs.
My students really enjoyed this activity and said that it was very helpful in helping them understand this concept.