Chapter 13.4, Problem 3PSA

(a)

To determine

To plot: The graph of given inequality.

Answer to Problem 3PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $y\ge \left|x+1\right|$ .

Graph is described as:

  $\begin{array}{c}y\ge \left|x+1\right|\\ 0\ge \left|0+1\right|\\ 0\ge 1\left[\text{false}\right]\end{array}$

The graph is shaded above.

The table for the line graph $y=\left|x+1\right|$ is given as:

$x$	$0$	$-1$
$y$	$1$	$0$

The graph is given as:

  

Therefore, the graph is shown above.

(b)

To determine

To plot: The graph of given inequality.

Answer to Problem 3PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $\left\{\left(x,y\right):x>2\text{or}x<-\text{1}\right\}$ .

Graph is described as:

  $\begin{array}{c}0>2\left[\text{false}\right]\\ \text{or}0<-\text{1}\left[\text{false}\right]\end{array}$

The graph is shaded left and right to the graph lines.

The graph is given as:

  

Therefore, the graph is shown above.

(c)

To determine

To plot: The graph of given inequality.

Answer to Problem 3PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $\left\{\left(x,y\right):5<y<7\right\}$ .

Graph is described as:

  $\begin{array}{c}5<0\left[\text{false}\right]\\ 0<7\left[\text{true}\right]\end{array}$

The graph is shaded intersection of above $5<y$ and below $y<7$ .

The graph is given as:

  

Therefore, the graph is shown above.

(d)

To determine

To plot: The graph of given inequality.

Answer to Problem 3PSA

The graph is shown below.

Explanation of Solution

Given:

The given inequality is:

  $\left\{\left(x,y\right):\left|x\right|<3\right\}$ .

Graph is described as:

  $\begin{array}{c}\left|x\right|<3\\ -3<x<3\\ -3<0<3\left[\text{true}\right]\end{array}$

The graph is shaded inside the graph lines.

The graph is given as:

  

Therefore, the graph is shown above.