Chapter 7.4, Problem 5E

Solution

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

Graph (e); Boundary is included from the graph.

Given Information:

The inequality is $y\ge 2-x^2$ .

Explanation:

Consider the given inequality, $y\ge 2-x^2$ .

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

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

Check for the point $\left(2,4\right)$ if it is the solution of the inequality.

  $\begin{array}{l}4\stackrel{?}{\ge }2-{\left(2\right)}^2\\ 4\stackrel{?}{\ge }2-4\\ 4\ge -2\end{array}$

So, the point $\left(2,4\right)$ is the solution of the given inequality.

Draw the graph of $y\ge 2-x^2$ .

  

The graph of $y\ge 2-x^2$ is the graph of parabola consisting of all the points on and above the boundary of the parabola.

Therefore, the given inequality matches with the graph (e) and boundary is included from the graph.