Chapter 3.3, Problem 7CFU

To determine

To graph: the given inequality.

Explanation of Solution

Given information:

  $y\le {\left(x+1\right)}^3$

Calculation:

The line equation of the inequality can be written as follows:

  $y={\left(x+1\right)}^3$..........(1)

Make a table of values for line equation of (1) as follows:

$x$	$-3$	$-2$	$-1$	0	1	2	3	4
$y$	$-8$	$-1$	0	1	8	27	64	125

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

Check the true point for inequality is as follows:

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

The graph of the given inequality and shade the region satisfying the inequality as follows: