Effect of y² and 1/y on oblique asymptotes

[qazxsw11111]

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.

 

[willem2]

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 ?

 

[qazxsw11111]

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?

 

[willem2]

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 $\sqrt{f(x)}$ ?