Chapter 1.2, Problem 37E

Solution

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

It is bounded below.

Given information: 

The function $y=2^x$ .

Calculation:

Graph of

  $y=2^x$

Putting the value of $x=0$ then $y=1$ .

And $x=-2$ , $y=0.25$

And $x=-1$ , $y=0.5$

And $x=1$ , $y=2$

And $x=2$ , $y=4$

And $x=3$ , $y=8$

And $x=\infty$ , $y=\infty$

And $x=-\infty$ , $y=0$

Plot the graph:

  

We see the function is bounded below, as it never goes below $y=0$ .

Hence, the function is bounded below.