Question

How do you find the vertical, horizontal and slant asymptotes of: `arctanx`?

Answer 1

Horizontal asymptotes at `y=pi/2` and `y=-pi/2`.

Explanation:

Of the types of asymptotes a function can have, the graph of arctangent only has horizontal asymptotes. They're located at `y=pi/2` and `y=-pi/2`.

The limited one-to-one graph of tangent that we use to define arctangent has domain `-pi/2 < x < pi/2` and has vertical asymptotes at `x=pi/2` and `x=-pi/2`. When we create the inverse function the vertical asymptotes become the horizontal asymptotes.