# 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

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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Micah Hobbs
The function $f\left(x\right)=ax+b$ obviously has asymptote $y=ax+b$. To make things not that trivial, you may add things that shrink to 0 when $x\to \mathrm{\infty }$. For example, the function
$f\left(x\right)=ax+b+\frac{1}{x+1}$
will also have $y=ax+b$ as asymptote. It is easy to see that you can find rational functions that have asymptote $y=ax+b$ using this method.