Question

Which of the following are vertical asymptotes of the function y=3cot(2x) - 4? Check all that apply.

Answer 1

Given the function:

$y=3cot(2x)-4$

Let's find the vertical asymptotes of the function.

To find the vertical asymptote, set 2x equal to zero:

$2x=0$

Solve for x.

To solve, divide both sides by 2:

$\begin{gathered} \frac{2x}{2}=\frac{0}{2} \\ \\ x=0 \end{gathered}$

Also, term inside the cotangent function, (2x), to π:

$2x=\pi$

Solve for x by dividing both sides by 2:

$\begin{gathered} \frac{2x}{2}=\frac{\pi}{2} \\ \\ x=\frac{\pi}{2} \end{gathered}$

Also, apply the trigonometric identity:

$cot=\frac{cos}{sin}$

Hence, the vertical asymptote will be where sin(2x) equals 0.

Now, input all given choices for x in sin(2x) and solve:

$\begin{gathered} sin(2*\frac{\pi}{3})=0.86 \\ \\ sin(2*\frac{\pi}{2})=sin\pi=0 \\ \\ sin(2*2\pi)=sin4\pi=0 \\ \\ sin(\pi)=0 \end{gathered}$

Therefore, the vertical asymptotes of the given function are:

$\begin{gathered} x=\pm\frac{\pi}{2} \\ \\ x=2\pi \\ \\ x=\pi \end{gathered}$

ANSWER:

B. x = ±π/2

C. x = 2π

D. x = π