Math CentralQuandaries & Queries


Question from Kendall, a teacher:

If a compound function is defined as 1/x for x<0 and 5 for x>=0 does it have a vertical asymptote at x=0? According to the definition in my book I think it does because the left-hand limit is infinity and it only takes one side to cause a vertical asymptote. Thanks!

Hi Kendall,

You did exactly what I would have done, you checked to see what the textbook author has as a definition. I also looked in three books on my shelf and they all agree that there is a vertical asymptote if either the right-hand or left-hand limits approach plus or minus infinity.


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