Chapter 1.2, Problem 40E

Solution

Whether the function is bounded above, bounded below, or bound in its territory.

It is bounded on its domain.

Given information: 

The function $y=x-x^3$ .

Calculation:

Graph of

  $y=x-x^3$

Putting the value of $x=0$ then $y=\sqrt{1}$ .

And $x=-1$ then $y=2$

Plot the graph:

  

The function is unbounded, that is, it is not bounded above or below.

However, we see that it is bounded below in the interval $(-\infty ,0]$ and bounded above in the interval $[0,\infty )$ .

Hence, the function is bounded on its domain.