graph the following function. show at least two cycles. use the graph to determine the domain and range of…

Explanation:

Step1: Recall secant function definition

The secant function is defined as $\sec x=\frac{1}{\cos x}$. The cosine - function $\cos x = 0$ when $x=\frac{(2k + 1)\pi}{2},k\in\mathbb{Z}$ (where $k$ is an integer). Since $\sec x=\frac{1}{\cos x}$, the function $y = 8\sec x$ is undefined when $\cos x = 0$. So the domain of $y = 8\sec x$ is $\left{x|x\neq\frac{k\pi}{2},k\text{ is an odd integer}\right}$.

Step2: Analyze the range of the secant function

The range of the basic secant function $y=\sec x$ is $(-\infty,- 1]\cup[1,\infty)$. For the function $y = 8\sec x$, we multiply the output values of $y=\sec x$ by 8. So the range of $y = 8\sec x$ is $(-\infty,-8]\cup[8,\infty)$.

Answer:

A. $\left{x|x\neq\frac{k\pi}{2},k\text{ is an odd integer}\right}$ $(-\infty,-8]\cup[8,\infty)$