question find the equation of the vertical asymptotes of the trigonometric function below in general form…

question find the equation of the vertical asymptotes of the trigonometric function below in general form (for all real values of x). express your answers as a single equation in terms of k, as determined by the dropdown below. f(x)=2tan(1/4πx) answer attempt 1 out of 2 equation: where k is a whole number where k is a rational number where k is a real number where k is an integer

question find the equation of the vertical asymptotes of the trigonometric function below in general form (for all real values of x). express your answers as a single equation in terms of k, as determined by the dropdown below. f(x)=2tan(1/4πx) answer attempt 1 out of 2 equation: where k is a whole number where k is a rational number where k is a real number where k is an integer

Answer

Explanation:

Step1: Recall tangent - asymptote property

The tangent function $y = \tan(t)$ has vertical asymptotes at $t=\frac{\pi}{2}+n\pi$, where $n$ is an integer. For the function $f(x)=2\tan(\frac{1}{4}\pi x)$, set $\frac{1}{4}\pi x=\frac{\pi}{2}+k\pi$.

Step2: Solve for $x$

First, multiply both sides of the equation $\frac{1}{4}\pi x=\frac{\pi}{2}+k\pi$ by $\frac{4}{\pi}$. We get $x = 2 + 4k$.

Answer:

$x=2 + 4k$, where $k$ is an integer