Effect of y² and 1/y on oblique asymptotes

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Homework Help Overview

The discussion revolves around the effects of transformations, specifically 1/y and y², on the presence of oblique asymptotes in the context of graphs represented by y = f(x).

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of transforming a function on its oblique asymptotes, questioning whether such transformations lead to the disappearance of these asymptotes. There is also confusion regarding the definition of transformations and the nature of the graphs involved.

Discussion Status

The conversation is ongoing, with participants seeking clarification on the original question and confirming assumptions about the behavior of oblique asymptotes under specific transformations. Some guidance has been offered regarding the conditions for oblique asymptotes, but no consensus has been reached.

Contextual Notes

There appears to be some ambiguity in the terminology used, particularly regarding what constitutes a transformation and the specific types of functions being discussed. Participants are also navigating the implications of limits in relation to oblique asymptotes.

qazxsw11111
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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 [tex]\lim_{x->+\infty} \frac {f(x)} {x} = C[/tex] for some constant C>0.

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

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