Chapter 7.4, Problem 4E

Solution

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

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

Given Information:

The inequality is $y>\left(1/2\right)x^2-1$ .

Explanation:

Consider the given inequality, $y>\left(1/2\right)x^2-1$ .

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 $y=\left(1/2\right)x^2-1$ .

Check for the point $\left(0,1\right)$ if it is the solution of the inequality.

  $\begin{array}{l}1\stackrel{?}{>}\frac{1}{2}{\left(0\right)}^2-1\\ 1\stackrel{?}{>}0-1\\ 1>-1\end{array}$

So, the point $\left(0,1\right)$ is the solution of the given inequality.

Draw the graph of $y>\left(1/2\right)x^2-1$ .

  

The graph of $y>\left(1/2\right)x^2-1$ is the graph of parabola consisting of all the points above the parabola.

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