which is an asymptote of the graph of the function $y = \\tan(\\frac{3}{4}x)$?\n$x=-\frac{4pi}{3}$\n$x =…

Explanation:

Step1: Recall tangent - asymptote formula

The asymptotes of the tangent function $y = \tan(u)$ occur when $u=(2n + 1)\frac{\pi}{2}$, where $n$ is an integer. For the function $y=\tan(\frac{3}{4}x)$, we set $\frac{3}{4}x=(2n + 1)\frac{\pi}{2}$.

Step2: Solve for $x$

Multiply both sides of the equation $\frac{3}{4}x=(2n + 1)\frac{\pi}{2}$ by $\frac{4}{3}$. We get $x=\frac{4}{3}(2n + 1)\frac{\pi}{2}=\frac{2(2n + 1)\pi}{3}$.

Step3: Find a specific asymptote

Let $n=- 1$. Then $x=\frac{2(-2 + 1)\pi}{3}=-\frac{2\pi}{3}$.

Answer:

$x =-\frac{2\pi}{3}$