Can asymptotes be any straight line? I was thinking if graphs can have asymptotes as x=y or any other random line . I couldn't think of a function . please help

Marcus Bass 2022-09-19 Answered
Can asymptotes be any straight line?
I was thinking if graphs can have asymptotes as x=y or any other random line . I couldn't think of a function . please help
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Answers (1)

Micah Hobbs
Answered 2022-09-20 Author has 8 answers
The function f ( x ) = a x + b obviously has asymptote y = a x + b. To make things not that trivial, you may add things that shrink to 0 when x . For example, the function
f ( x ) = a x + b + 1 x + 1
will also have y = a x + b as asymptote. It is easy to see that you can find rational functions that have asymptote y = a x + b using this method.

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