Chapter 1.4, Problem 15E

a.

To determine

Find an appropriate viewing rectangle for the given function.

Answer to Problem 15E

  

Explanation of Solution

Given information:

Try to find an appropriate viewing rectangle for $f\left(x\right)={\left(x-10\right)}^3{2}^{-x}$ .

Calculation:

As, there is no single appropriate viewing window for $y={\left(x-10\right)}^3{2}^{-x}$ , as the graph has a lot of complicated activity in the region $5<x<35$ that is too complicated to be seen in any window that also shows a reasonable approximation of the end behavior of the graph. We can instead use two viewing windows, one showing the complex local region and one showing an overview of the graph’s behavior. Now, the first window should be defined by $5<x<35$ and $-0.003<y<0.004$ , will look like this:

  

Now, the second window should show the end behavior and general shape of the graph on a larger scale. Use $-10<x<50$ and $-200<y<200$ which looks like this:

  

Hence, the result shown in graph.

b.

To determine

Do you need more than one window? Why?

Answer to Problem 15E

Two windows are necessary because complicated region around $\boxed{x=15}$.

Explanation of Solution

Given information:

Do you need more than one window? Why?

Calculation:

Here, two windows are necessary because the end behavior of the graph is visible only on a scale that makes it impossible to view the small complicated region around $\boxed{x=15}$.