horizontal asymptotes
I'm not really sure if I understand how to find the horizontal asymptotes correctly. For #62, in section 4.5, is the horizontal asymptote y=50 because for questions 19, 29, and 31 i did not get the correct value for the asymptote.
posted by Anonymous at 6:18 PM
2 Comments:
Yes, it is 50 (At least I think, I'm not very reliable).A horizontal asymptote is the maximum that y is equal to. use Jake's rule when possible. The highest degree term is the one you want to focus on, because everything else becomes insignificant. because with something like x^2-5x, as x gets huge, the difference between these two gets so large that 5x is essentially zero in coparison to x^2.
Since the graph of the function is 50x/(x-50), the asymptote would be 50. As x gets bigger, the difference between x and x-50 becomes negligible, so it becomes more and more like dividing 50x by x, and therefore the y value becomes closer and closer to 50. Also, if this is still confusing you can always just plug in very large numbers for x on your calculator until the resulting values stop increasing.
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