Chapter 4.4, Problem 30PPE

To determine

To graph: The equation $y=\left|-2x\right|-1$ on the graph paper.

Explanation of Solution

Given:

The equation is $y=\left|-2x\right|-1$ .

Calculation:

Break the absolute function $y=\left|-2x\right|-1$ as $y=2x-1$ and $y=-2x-1$ .

Substitute $x=0$ in the equation $y=2x-1$ to obtain the value of $y$ as follows:

  $\begin{array}{c}y=2\left(0\right)-1\\ =0-1\\ =-1\end{array}$

Substitute $x=1$ in the given equation $y=2x-1$ to obtain the value of $y$ as follows:

  $\begin{array}{c}y=2\left(1\right)-1\\ =2-1\\ =1\end{array}$

Substitute $x=-2$ in the given equation $y=-2x-1$ to obtain the value of $y$ as follows:

  $\begin{array}{c}y=-2\left(-2\right)-1\\ =4-1\\ =3\end{array}$

Substitute $x=-1$ in the given equation $y=-2x-1$ to obtain the value of $y$ as follows:

  $\begin{array}{c}y=-2\left(-1\right)-1\\ =2-1\\ =1\end{array}$

Substitute the obtained values in the table given below.

$x$	$y$
0	$-1$
1	1
$-2$	$3$
$-1$	1

Plot the points and join them to obtain the graph as follows: