Question

What are the horizontal asymptotes of \[y=\tan^{-1}x\]?

Options

• \[y=0\] and \[y=\frac{\pi}{2}\]

• \[y=0\] and \[y=\pi\]

• \[y=-\frac{\pi}{2}\] and \[y=\frac{\pi}{2}\]

• \[y=-\pi\] and \[y=\pi\]

Answer 1

The range of \[y=\tan^{-1}x\] lies strictly between \[-\frac{\pi}{2}\] and \[\frac{\pi}{2}\]. Therefore these two lines are its horizontal asymptotes.