Reciprocal of a cubic function

AI Thread Summary
The discussion centers on the possibility of a cubic function having a reciprocal without vertical asymptotes. It concludes that if a reciprocal lacks vertical asymptotes, the cubic function must have no roots, which is impossible. Therefore, all reciprocal functions derived from cubic functions will inherently have vertical asymptotes. This aligns with the mathematical properties of cubic functions and their reciprocals. Ultimately, no cubic function can exist without roots that would prevent vertical asymptotes in its reciprocal.
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Is it possible to have the reciprocal of a cubic function that does not have any vertical asymptotes?
 
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If the reciprocal has no vertical asymptotes, then the cubic function would have no roots. No such cubic exists.
 
Yeah.. thought so. I guess for all reciprocal functions, there will always be a vertical asymptote.
 

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