\[ y=4 \cot \left(\frac{1}{2} x\right) \] Drag the movable red point to set the vertical asymptotes (dashed red lines) for one period of the given function. Also place the blue point at the correct set of coordinates.

1. The function is given by \[ y = 4 \cot\left(\frac{1}{2}x\right). \] 2. For the cotangent function, vertical asymptotes occur when its argument is an integer multiple of \(\pi\), i.e. when \[ \cot\theta \quad \text{is undefined for} \quad \theta = k\pi, \quad k\in\mathbb{Z}. \] Here, the argument is \(\frac{1}{2}x\), so set \[ \frac{1}{2}x = k\pi. \] Solving for \(x\) gives \[ x = 2k\pi. \] 3. Choosing one period of the function, select two adjacent vertical asymptotes. For instance, take \[ k=0 \quad \text{and} \quad k=1. \] This places the vertical asymptotes at \[ x=0 \quad \text{and} \quad x=2\pi. \] Drag the movable red points to these \(x\)-values. 4. The cotangent function passes through zero exactly midway between its vertical asymptotes. The midpoint of \(x=0\) and \(x=2\pi\) is \[ x = \frac{0+2\pi}{2} = \pi. \] Substitute \(x=\pi\) into the function: \[ y = 4 \cot\left(\frac{1}{2}\pi\right) = 4\cot\left(\frac{\pi}{2}\right). \] Since \(\cot\left(\frac{\pi}{2}\right)=0\), we have \[ y = 0. \] Place the blue point at the coordinate \[ (\pi, 0). \]