what is the range of the function y = cot(x)?\no all real numbers\no all real numbers except…

Explanation:

Step1: Recall the definition of cotangent

The cotangent function is defined as $\cot(x)=\frac{\cos(x)}{\sin(x)}$.

Step2: Analyze the behavior of the function

As $x$ varies, $\sin(x)$ can take values from - 1 to 1. The function $\cot(x)$ is well - defined for all $x$ such that $\sin(x)\neq0$. The values of $x$ for which $\sin(x) = 0$ are $x = n\pi$, where $n\in\mathbb{Z}$. But when considering the range, we know that as $x$ approaches values where $\sin(x)\to0$ and $\cos(x)\neq0$, $\cot(x)$ approaches $\pm\infty$. And as $x$ varies continuously, $\cot(x)$ can take on any real - valued output. So the range of $y = \cot(x)$ is all real numbers.

Answer:

A. all real numbers