In this pencast I find a function that satisfies a particular condition — the function should have a vertical asymptote at x=1 and a horizontal asymptote at y=2.
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This was good to watch. The concept behind these problems is simple but it is hard to find functions when you are given so little information. I think it helps to keep things as simplified as possible in your mind or else you can get overwhelmed by the tremendous amount of possibilities there are when coming up with functions.
I totally agree with ZOGBY (from Oct 16th, 2009). I found this to be extremely true today when I came across a set of exam questions related to a function where the only information given was that f(x)=x and f(-x)=-x. These statements could be true in reference to many functions with any number of transformations, so coming up with possible functions to fit this criteria took imagination with restraint against going too crazy.
However, after watching this pencast, I realize that I may have made answering this set of exam questions harder than it needed to be. I now see that coming up with examples to fit these criteria could have been really simple.
This pencast was pretty useful. There are times where I mix up the problems on either the homework or exam and have to rework them, wasting time, which is especially significant during tests, simply by complicating a problem. Keeping things simple reduces the number of steps which in turn reduces the number of occasions which one can make a careless mistake.