Chapter 10.1, Problem 27E

Solution

To find: The graph, domain, range and period of the function $y=\sec x$ .

Domain: $\left\{\text{all real }x:x\ne \frac{n}{2}+n\pi ,n\in Z\right\}$

Range: $\left(-\infty ,-1\right]\cup \left[1,\infty \right)$

Period: $2\pi$

Given information:

The function $y=\sec x$

Graph:

The domain of $y=\sec x$ is given by,

  $\left\{\text{all real }x:x\ne \frac{n}{2}+n\pi ,n\in Z\right\}$

The range of $y=\sec x$ is given by,

  $\left(-\infty ,-1\right]\cup \left[1,\infty \right)$

The period of $y=\sec x$ is given by,

  $2\pi$

The graph of $y=\sec x$ is,