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

1 Answer
Jan 14, 2018

Answer:

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.