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

Marcus Bass

Answered question

2022-09-19

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

Answer & Explanation

Micah Hobbs

Micah Hobbs

Beginner2022-09-20Added 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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