Chapter 4.5, Problem 3E

Solution

To identify: The graph of the functions $\csc x$ and $3\csc 2x$ from the given figure.

The graph of the function $\csc x$ is represented by $y_2$ and the graph of the function $3\csc 2x$ is represented by $y_1$ .

Given information: The graph of two periods of $\csc x$ and $3\csc 2x$ is shown below.

  

Figure (1)

Explanation:

The graph of the function $y=\csc x$ is horizontally shrunk by $2$ units and stretched vertically by $3$ units to obtain the graph of the function $y=3\csc 2x$ .

From the figure it can be observed that the graph of function $y_2$ is stretched vertically and shrunk horizontally to form of the graph of the function $y_1$ .

Thus, the graph of the function $\csc x$ is represented by $y_2$ and the graph of the function $3\csc 2x$ is represented by $y_1$ .