What are the horizontal asymptotes of cot^-1(x)?

[kirbykirbykirby]

What are the horizontal asymptotes of
cot^(-1)x
I don't understand because isn't that tangent and it has asymptotes?!

 

[kirbykirbykirby]

So.. why is arccotangent cot(1/x)... I don't understand.

 

[HallsofIvy]

It isn't. It also is not 1/cot(x) which is tan(x).

When working with functions, the "exponent" -1 does not mean "reciprocal" (and isn't really an exponent). It means "inverse function".

cot^-1(x) is just another notation for arccot(x), the inverse function to cot(x).
Specifically, if y= cot^-1(x)= arccot(x), then x= cot(y). Notice that you have swapped x and y so the graphs will swap x and y axes. Where does cotangent have vertical asymptotes?