Chapter 11, Problem 82RE

To determine

Graph each inequality.

Answer to Problem 82RE

Explanation of Solution

Given information:

Graph each inequality.

  $x\ge y^2$

Calculation:

Consider the given inequality,

  $x\ge y^2$

Now replace inequality sign $\ge$ with $=$ and find the equation,

  $x=y^2$ Now graph this equation.

Test the point $\left(0,0\right)$ on the given inequality as,

  $\begin{array}{l}0\ge 0^2\\ 0\ge 0\end{array}$

It is true that $0\ge 0$ so $\left(0,0\right)$ is the solution of inequality.

So the solution of $x\ge y^2$ are given by the point in the half-plane to the right of the curve and the graph is sketched in the rectangular Cartesian coordinate system as given below,

Hence, the inequality graph is as shown.