Chapter 3.3, Problem 8MCQ

To determine

To graph: the given inequality.

Answer to Problem 8MCQ

  

Explanation of Solution

Given information:

  $y\ge {\left(\frac{1}{3}x\right)}^2+2$

Calculation:

Make a table of values for line equation $y={\left(\frac{1}{3}x\right)}^2+2$ as follows:

$x$	$-3$	$-2$	$-1$	0	1	2	3	4
$y$	3	$\frac{22}{9}$	$\frac{19}{9}$	2	$\frac{19}{9}$	$\frac{22}{9}$	3	$\frac{34}{9}$

Plot these points for the equations and test the true points to shade the region of inequality. Since the inequality has greater than or equal to sign so, the graph will have solid line.

Check the test point for inequality as follows:

Test point	$y\ge {\left(\frac{1}{3}x\right)}^2+2$	True or False
$\left(0,0\right)$	$\begin{array}{l}0\ge {\left(\frac{1}{3}\left(0\right)\right)}^2+2\\ 0\ge 0+2\\ 0\ge 2\end{array}$	False
$\left(0,3\right)$	$\begin{array}{l}3\ge {\left(\frac{1}{3}\left(0\right)\right)}^2+2\\ 3\ge 0+2\\ 3\ge 2\end{array}$	True

The graph of the given inequality is as follows: