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The first question of the test asks you to sketch the reciprocal of a function f(x) and label any asymptotes and points of invarience. This function went from negative infinity, to 4, then back down to about -2, and the graph indicated that it continued on, never quite reaching -2.

Vertical asymptotes are easy enough; where it crosses 0. However, there are apparently 2 horizontal asymptotes, one at -1/2, and one at 0. The 0 makes sense, NO WHERE on the reciprical function does the graph cross 0; that is impossible. The -1/2 does not make sense. As I said, the ealrier part of the function comes all the way up from negative infinity with no breaks in the graph, therefore it DOES pass -2 and this the reciprocal does cross -1/2. I asked the teacher (this was at the end of class, so I did not have much time to make my point because I had to go to my next class) and he was saying something about local asymptotes, a concept that I was never introduced to. I was always taught that asymptotes were lines a function would never cross.

Am I wrong?