Chapter 7.4, Problem 6E

Solution

Match the inequality with the graphs and indicate whether the boundary is included or excluded from the graph.

Graph (a); Boundary is excluded from the graph.

Given Information:

The inequality is $x^2+y^2<4$ .

Explanation:

Consider the given inequality, $x^2+y^2<4$ .

Write the equation of the obtained inequality by replacing the sign “ $<$ ” with the “ $=$ ”. The inequality sign $<$ will indicate that the graph should be drawn with a dashed line.

The obtained equation will be $x^2+y^2=4$ .

Check for the point $\left(1,1\right)$ if it is the solution of the inequality.

  $\begin{array}{l}{1}^2+1^2\stackrel{?}{<}4\\ 1+1\stackrel{?}{<}4\\ 2<4\end{array}$

So, the point $\left(1,1\right)$ is the solution of the given inequality.

Draw the graph of $x^2+y^2<4$ .

  

The graph of $x^2+y^2<4$ is the graph of circle consisting of all the points inside the boundary of a circle.

Therefore, the given inequality matches with the graph (a) and boundary is excluded from the graph.