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Example. What happens to ( f(x) ) as ( x ) goes through larger and larger positive numbers? Larger and larger negative numbers?I am learning

Example. What happens to \( f(x) \) as \( x \) goes through larger and larger positive numbers? Larger and larger negative numbers?I am learning calculus online, and I have this screen shot from a webinar I can't find any longer. I would really like to know how to express this graph mathematically. If you can take a look and see if you can identify this and write an expression for it, I'd appreciate it. (The horizontal Asymptotes are 2 and 1, as drawn in as red dots) The goal is for me to tweak the functions and play around with the variables to change the nature of the graph, but I need to know the expression first.

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