$\text { Find the vertical asymptotes (if any) of the function } f ( x ) = \tan ( 15 x ) \text {. }$
A) $x = \frac { k } { 15 } \pi ( k = 0 , \pm 1 , \pm 2 , \ldots )$
B) $x = \frac { 2 k + 1 } { 30 } \pi ( k = 0 , \pm 1 , \pm 2 , \ldots )$
C) $x = \frac { 2 k } { 15 } \pi ( k = 0 , \pm 1 , \pm 2 , \ldots )$
D) $x = \frac { 2 k + 1 } { 15 } \pi ( k = 0 , \pm 1 , \pm 2 , \ldots )$
E) no vertical asymptotes

Question

$\text { Find the vertical asymptotes (if any) of the function } f ( x ) = \tan ( 15 x ) \text {. }$ 
A) $x = \frac { k } { 15 } \pi ( k = 0 , \pm 1 , \pm 2 , \ldots )$
B) $x = \frac { 2 k + 1 } { 30 } \pi ( k = 0 , \pm 1 , \pm 2 , \ldots )$
C) $x = \frac { 2 k } { 15 } \pi ( k = 0 , \pm 1 , \pm 2 , \ldots )$
D) $x = \frac { 2 k + 1 } { 15 } \pi ( k = 0 , \pm 1 , \pm 2 , \ldots )$
E) no vertical asymptotes

Quizplus · Accepted Answer

The tangent function, $\tan(x)$, has vertical asymptotes at $x = \frac{\pi}{2} + k\pi$ for any integer $k$. For $\tan(15x)$, the argument $15x$ equals $\frac{\pi}{2} + k\pi$ when $x = \frac{\pi}{2 \cdot 15} + \frac{k\pi}{15}$, simplifying to $x = \frac{2k + 1}{30}\pi$, where $k$ is any integer.

Find the vertical asymptotes (if any) of the function f(x)=tan⁡(15x). \text { Find the vertical asymptotes (if any) of the function } f ( x ) = \tan ( 15 x ) \text {. } Find the vertical asymptotes (if any) of the function f(x)=tan(15x).

$\text { Find the vertical asymptotes (if any) of the function } f ( x ) = \tan ( 15 x ) \text {. }$