Chapter 6.3, Problem 4BGP

To determine

To plot: The graph of the given inequality.

Answer to Problem 4BGP

The graph of the given inequality is given below.

Explanation of Solution

Given:

The given inequality function is:

  $f\left(x\right)<-\sqrt{x+2}-4\dots \left(1\right)$

The value of what’s under the square root must be greater than equal to zero.

Therefore,

  $\begin{array}{c}x+2\ge 0\\ x\ge -2\end{array}$

So the domain is $\left\{x:x\ge -2\right\}$ .

The table for the graph of the function $f\left(x\right)=-\sqrt{x+2}-4$ is given as:

$x$	$-2$	$7$
$f\left(x\right)$	$-4$	$-7$

The graph of the given inequality function is given by:

  

Because $y$ is less than, so the shaded region must be lies below the boundary of the graph and within the domain.

Check:

Select a point in the shaded region and verify it is a solution of the inequality.

Test for the point $\left(40,-40\right)$

  $\begin{array}{c}-40<-\sqrt{40+2}-4\\ -40<-10.48\left[\text{True}\right]\end{array}$