Chapter 9.5, Problem 35E

To determine

To calculate; why there is more than one tangent function whose graph passes through origin and has asymptotes at $x=\pi$ and $x=-\pi .$

Answer to Problem 35E

Solution: $g(x)=\tan (\frac{x}{2}),g(x)=2\tan (\frac{x}{2})$

Explanation of Solution

While calculating aysmpototes of the equation in the form $g(x)=a\tan bx$ , the formula goes by $(\frac{\pi }{2\left|b\right|},-\frac{\pi }{2\left|b\right|})$ which is dependent on variable $b.$

Hence there can be more than one tangent function function whose graph passes through origin and has asymptotes at $x=\pi$ and $x=-\pi .$

For example:- $g(x)=\tan (\frac{x}{2}),g(x)=2\tan (\frac{x}{2})$