Chapter 9.5, Problem 48E

a.

To determine

Find the period of the graph.

Answer to Problem 48E

  $T=4$

Explanation of Solution

Given information:

  

Calculation:

Consider the graph,

  

Now calculate period of the graph,

  $\begin{array}{l}T=2-\left(-2\right)\\ T=4\end{array}$

Hence, period is $T=4$ .

b.

To determine

Find the range of the function.

Answer to Problem 48E

  $\left(-\infty ,-2\right]\cup \left[2,\infty \right)$

Explanation of Solution

Given information:

  

Calculation:

Consider the graph,

  

Now calculate range,

  $\left(-\infty ,-2\right]\cup \left[2,\infty \right)$

Hence, range is $\left(-\infty ,-2\right]\cup \left[2,\infty \right)$ .

c.

To determine

Explain the function of the form $f(x)=a\csc bx$ or $f(x)=a\sec bx$ .

Answer to Problem 48E

  $f\left(x\right)=a\csc bx$

Explanation of Solution

Given information:

  

Calculation:

The function has the asymptote $x=0$ . The function that is not defined for $x=0$ is $\csc x$ .

Hence, the function is in the form $f\left(x\right)=a\csc bx$