Effect of y² and 1/y on oblique asymptotes

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Transforming a graph of y = f(x) to either 1/y or y² results in the disappearance of oblique asymptotes, as these transformations change the nature of the function. The discussion seeks confirmation on whether oblique asymptotes can still exist when replacing f(x) with 1/f(x) or √f(x). It is noted that for an oblique asymptote to exist, the limit condition involving f(x) must hold true. Participants express confusion about the transformations and their implications on asymptotic behavior. Overall, the consensus leans towards the idea that oblique asymptotes do not persist under these transformations.
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Hi everyone. If I have a y= graph and I do a transformation of either 1/y or y², the oblique asymptotes will disappear as they are no longer 'oblique'. Is that correct.

A simple yes or no would suffice.

Enjoy your day.
Thanks.
 
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I don't unterstand the question. I suppose what you mean with an 'y=' graph is a graph of of y = f(x). What is a transformation of 1/y ?
 
Effect of a oblique asymptote on the y=f(x) graph tranformed into 1/f(x) graph and y² graph. I assume the oblique asymptotes will be gone. Will someone confirm?
 
to get an oblique asymptote on the right, you must have \lim_{x->+\infty} \frac {f(x)} {x} = C for some constant C>0.

Is this still possible if you replace f(x) with 1/f(x) or \sqrt{f(x)} ?
 

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