Chapter 7, Problem 1T

To determine

To Graph: The graph of the function $y=\left|x\right|-2$, for $x=-3,-2,-1,0,1,2,\text{ and 3}\text{.}$

Explanation of Solution

Given:

The given function is $y=\left|x\right|-2$, where $x=-3,-2,-1,0,1,2,\text{ and 3}\text{.}$

Graph:

The Graph of the function is as shown below:

Interpretation:

In the given above expression, find the values of the function for each value of $x$.

For $x=-3$,

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

The point is $\left(-3,1\right)$.

For $x=-2$,

$\begin{array}{c}y=\left|-2\right|-2\\ =0\end{array}$

The point is $\left(-2,0\right)$.

For $x=-1$,

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

The point is $\left(-1,-1\right)$.

For $x=0$,

$\begin{array}{c}y=\left|0\right|-2\\ =-2\end{array}$

The point is $\left(0,-2\right)$

For $x=1$,

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

The point is $\left(1,-1\right)$

For $x=2$,

$\begin{array}{c}y=\left|2\right|-2\\ =0\end{array}$

The point is $\left(2,0\right)$

For $x=3$,

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

The point is $\left(3,1\right)$

Therefore, the points will be $\left(-3,1\right),\left(-2,0\right),\left(-1,-1\right),\left(0,-2\right),\left(1,-1\right),\text{ and}\left(3,1\right)$.

Hence, the graph of the function corresponding to the points is as shown above: