Chapter 1.8, Problem 32E

To determine

To graph: The region provided by the set $\left\{\left(x,y\right)|\left|x\right|\le 2\text{ and }\left|y\right|\le 3\right\}$ .

Explanation of Solution

Given information:

The set, $\left\{\left(x,y\right)|\left|x\right|\le 2\text{ and }\left|y\right|\le 3\right\}$ .

Graph:

The graph of the region provided by the set $\left\{\left(x,y\right)|\left|x\right|\le 2\text{ and }\left|y\right|\le 3\right\}$ is sketched in the coordinate plane.

Recall that $\left|x\right|\le a$ is equivalent to $-a\le x\le a$ .

Therefore, $\left|y\right|\le 3$ is equivalent to $-3\le y\le 3$ .

And $\left|x\right|\le 2$ is equivalent to $-2\le x\le 2$ .

Construct horizontal lines $y=-3\text{ and }y=3$ and shaded the region between it.

Construct vertical lines $x=-2\text{ and }x=2$ and shaded the region between it.

Now, shade the common region that belong to both the conditions stated above.

The region obtained is provided below,

  

Interpretation:

The region provided by the set $\left\{\left(x,y\right)|\left|x\right|\le 2\text{ and }\left|y\right|\le 3\right\}$ is shaded region. The solid vertical line at $x=-2\text{ and }x=2$ also horizontal lines $y=-3\text{ and }y=3$ denote that they are included in the region. The region consists of all those points whose y-coordinate lie between $y=-3\text{ and }y=3$ and x-coordinate lie between $x=-2\text{ and }x=2$ .