Answer
The graph is shown below:
Work Step by Step
We have to plot the graph of $ f\left( x \right)=\left| x \right|$; put y in place of $ f\left( x \right)$ and evaluate the value of the y variable for each value of the x variable:
To find the value of the y-intercept, put $ x=0$ as given below:
$\begin{align}
& y=\left| x \right| \\
& =\left| 0 \right| \\
& =0
\end{align}$
To find the value of the y-intercept, put $ x=1$ as given below:
$\begin{align}
& y=\left| x \right| \\
& y=\left| 1 \right| \\
& y=1
\end{align}$
To find the value of the y-intercept, put $ x=2$ as given below:
$\begin{align}
& y=\left| x \right| \\
& =\left| 2 \right| \\
& =2
\end{align}$
To find the value of the y-intercept, put $ x=-1$ as given below:
$\begin{align}
& y=\left| x \right| \\
& y=\left| -1 \right| \\
& y=1
\end{align}$
To find the value of the y-intercept, put $ x=-2$ as given below:
$\begin{align}
& y=\left| x \right| \\
& =\left| -2 \right| \\
& =2
\end{align}$
Therefore, plot the intercepts $\left( 0,0 \right),\left( 1,1 \right)\text{,}\left( 2,2 \right)\text{,}\left( -1,1 \right)\text{, and }\left( -2,2 \right)$ and join these points in order to get the graph of the equation $ f\left( x \right)=\left| x \right|$.
So, in order to plot the graph of $ g\left( x \right)=-\left| x-2 \right|$, put y in place of $ g\left( x \right)$ and evaluate the value of the y variable for each value of the x variable:
To find the value of the y-intercept, put $ x=0$ as given below:
$\begin{align}
& y=-\left| x-2 \right| \\
& =-\left| 0-2 \right| \\
& =-\left| 2 \right| \\
& =-2
\end{align}$
To find the value of the y-intercept, put $ x=1$ as given below:
$\begin{align}
& y=-\left| x-2 \right| \\
& =-\left| 1-2 \right| \\
& =-\left| -1 \right| \\
& =-1
\end{align}$
To find the value of the y-intercept, put $ x=2$ as given below:
$\begin{align}
& y=-\left| x-2 \right| \\
& =-\left| 2-2 \right| \\
& =-\left( 0 \right) \\
& =0
\end{align}$
To find the value of the y-intercept, put $ x=3$ as given below:
$\begin{align}
& y=-\left| x-2 \right| \\
& y=-\left| 3-2 \right| \\
& y=-\left| 1 \right| \\
& y=-1
\end{align}$
To find the value of the y-intercept, put $ x=4$ as given below:
$\begin{align}
& y=-\left| x-2 \right| \\
& =-\left| 4-2 \right| \\
& =-\left| 2 \right| \\
& =-2
\end{align}$
Therefore, plot the intercepts $\left( 0,-2 \right),\left( 1,-1 \right)\text{,}\left( 2,0 \right)\text{,}\left( 3,-1 \right)\text{, and }\left( 4,-2 \right)$ and join these points in order to get the graph of equation $ g\left( x \right)=-\left| x-2 \right|$.
