what function is graphed below?\no (y = cot(x)-2)\no (y=\tan(x)-2)\no (y = cot(x)+2)\no (y=\tan(x)+2)

Explanation:

Step1: Recall properties of tangent and cotangent functions

The tangent function $y = \tan(x)$ has vertical - asymptotes at $x=\frac{\pi}{2}+k\pi,k\in\mathbb{Z}$, and the cotangent function $y=\cot(x)$ has vertical - asymptotes at $x = k\pi,k\in\mathbb{Z}$. The given graph has vertical asymptotes at $x = k\pi,k\in\mathbb{Z}$, so it is a transformation of the cotangent function.

Step2: Analyze the vertical shift

The standard cotangent function $y = \cot(x)$ passes through the point $(\frac{\pi}{2},0)$. In the given graph, when $x=\frac{\pi}{2}$, $y = - 2$. This means the graph of $y=\cot(x)$ is shifted down by 2 units.

Answer:

$y=\cot(x)-2$