Chapter 1.6, Problem 65E

Solution

a.

To graph the price as a function of month as a line graph.

Let $y$ and $x$ represent the price and the month, respectively.

Also, let $y=f(x)$ represents the relationship between $y$ and $x$ .

The given data points are plotted in a viewing window, with the prices along the $y$-axis and months along the $x$ -axis:

  

The points so obtained are joined by straight lines to get the line graph as:

  

b.

To determine the transformation that would give the price in Japanese yen when it is applied to the graph obtained in part a.

A vertical stretch is applied to the graph, by a factor of $133.73$ , to obtain the graph giving the prices in Japanese yen.

Concept Used:

Given a function $y=f\left(x\right)$ .

The graph of $y=af\left(x\right)$ is a vertical stretch of that of $y=f\left(x\right)$ by a factor of $a$ if $a>1$ .

Explanation:

The Delta air lines is a US based company. So, it is listed in US stock exchanges. That is, the data must be given in US dollars.

Now, as of now, $1$ US dollar equals $133.73$ Japanese yen.

So, the prices in US dollars must be multiplied with $133.73$ to get the same in Japanese yen.

That is, the transformation applied to $y=f\left(x\right)$ is $y=133.73f\left(x\right)$ .

That is, a vertical stretch is applied to the graph, by a factor of $133.73$ , to obtain the one giving the prices in Japanese yen.

Conclusion:

A vertical stretch is applied to the graph, by a factor of $133.73$ , to obtain the graph giving the prices in Japanese yen.