Q. 38 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The graph of the system of inequalities is 

Step 1. Graph of the inequality y 2 ≤ x

The graph of the inequality$y^2\le x$ can be plotted by graphing$y^2\le x$

Since the point $(1,0)$ satisfies the inequality,

therefore, it will be included in the shaded region.

Step 2. Graph of the inequality y ≥ x

The graph of the inequality $y\ge x$ can be plotted by plotting $y=x$

Since, the point $(1,0)$ does not satisfy the inequality, therefore it will not be included in the graph shaded.

Step 3. Final graph

The intersection of both the graphs of the inequalities gives the final graph.