Q. 37 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 35–42, graph each system of inequalities by hand 

$\left\{\begin{array}{l}y\ge x^2-4\\ y\le x-2\end{array}\right.$

Step-by-Step Solution

Answer

The graph of the system of inequalities is 

Step 1, Graph of the inequality y ≥ x 2 - 4

To graph the inequality$y\ge x^2-4$, graph the equation$y=x^2-4$

Since, $(0,0)$ satisfies the given inequality $y\ge x^2-4$,

therefore, it will be included in the shaded region.

Step 2. Graph of the inequality y ≤ x - 2

The graph of the inequality $y\le x-2$ will be plotted by graphing the line$y=x-2$

Since,$(0,0)$ satisfies the given inequality, therefore it will be included in the shaded region.

Step 3. Final graph

The intersection of both the graphs will give the final graph.