Functions - Similarities and Differences

If you were asked to create lists covering the similarities and differences between exponential, logarithmic, and rational functions, what would you have on your lists? I recently had to answer this question from the seat of a student and was surprised how long it took me to decide what to write down. When I talked with my students, they mostly went with the graphs (which I also did), but a few talked about the inverse. As a learner, I was not sure - which made me think about rubrics and I started asking myself what I would expect as a teacher. This is fairly new stuff for me, and any input would be more valuable than you can imagine.