Ben was in a great mood today. He was listening to music when I entered and he told me he had Art work today. I asked him if that was his way of asking if he could have some time to work on it and he said Yes. I told him that I wanted to accomplish one task today, and if we have time left over, he can work on his art project. He agreed. First I did a tutorial with paper and pencil on his desk. I explained to him the concept of asymptotes. That it is essentially an imaginary line that the graph approaches but doesn’t touch. I showed him both vertical and horizontal asymptotes and how that would affect the domain and range. Since the graph doesn’t exist at those locations, we have to skip over those values when stating the domain and range. The first problem I showed him had a horizontal asymptote at 3 and a vertical asymptote at -2. We recognized the graph extends toward negative and positive infinity but does not exist at those locations where the asymptote is. So instead of stating the domain is (-inf,inf), we had to say (-inf,-2) & (-2,inf). Similarly for the range instead of (-inf,inf), it’s (-inf,3) & (3,inf). Then I wrote a challenge problem on the board. Ben said he disliked these problems. I reminded him how GREAT he did on yesterday’s lesson, this just had some values we skip over. He worked through the problem and reached a solution. With the time left in class, I allowed him to listen to music and work on his art. It was nice to hear his music choices, I enjoy his style.