Chapter 4.5, Problem 13E

Solution

To identify: The graph of the function $y=-2\tan x$ from graphs given below. Also, give the values of $X\min$ and $X\max$ values for the viewing window in which graph is shown.

  

The graph of the function $y=-2\tan x$ is (a) with $X\min =-\pi$ and $X\max =\pi$ .

Given information:

The function $y=-2\tan x$ and graphs given below.

  

Explanation:

Consider the function $y=-2\tan x$ ,

At $x=0$ ,

  $\begin{array}{c}y=-2\tan 0\\ =-2\cdot 0\\ =0\end{array}$

Check the graphs where $\left(x,y\right)=\left(0,0\right)$ . Only the graph (a), satisfies the criteria.

It is known that the period of tangent is $\pi$ .

So, the graph (a) has two periods with $X\min =-\pi$ and $X\max =\pi$ .

Thus, the graph of the function $y=-2\tan x$ is (a) with $X\min =-\pi$ and $X\max =\pi$ .