Question

2 multiple choice 1 point graph the function. y = -tan 2x

Explanation:

Step1: Recall the general form of the tangent function

The general form of the tangent function is \(y = A\tan(Bx - C)+D\). For the function \(y =-\tan(2x)\), we have \(A=- 1\), \(B = 2\), \(C = 0\), and \(D=0\).

Step2: Find the period

The period of the tangent function \(y=\tan(Bx)\) is given by \(T=\frac{\pi}{|B|}\). Since \(B = 2\), the period \(T=\frac{\pi}{2}\).

Step3: Analyze the reflection

The coefficient \(A=-1\) reflects the graph of \(y = \tan(2x)\) about the \(x\) - axis.

Step4: Find the vertical asymptotes

For the function \(y=\tan(2x)\), the vertical asymptotes are found by solving \(2x=-\frac{\pi}{2}+k\pi\), \(k\in\mathbb{Z}\). So \(x =-\frac{\pi}{4}+\frac{k\pi}{2}\), \(k\in\mathbb{Z}\).

Answer:

The graph of \(y =-\tan(2x)\) has a period of \(\frac{\pi}{2}\), is a reflection of \(y=\tan(2x)\) about the \(x\) - axis, and has vertical asymptotes at \(x=-\frac{\pi}{4}+\frac{k\pi}{2}\), \(k\in\mathbb{Z}\).