Question

Sketch the region given by the set

$\left\{\left(x,y\right)\left|-4<x<4\text{and}-2<y<2\right.\right\}$

Short answer

The graph of the given set is shown in the below figure

Step-by-step solution

Step 1. Write the given set.

The given set is,

$\left\{\left(x,y\right)\left|-4<x<4\text{and}-2<y<2\right.\right\}$

In the given set the word between the two inequalities is “and”, this indicates the intersection of the graphs of inequalities.

Step 2. Interpret the given set.

The given set the indicates that values of x lie from$-4$ to 4 and the values of y lie from$-2$ to 2.

Step 3. Plot the graph.

Sketch the region of x and y respectively on the coordinate plane.

Figure (1)

Thus, the graph of the given set is shown in figure 1.