Precalculus (6th Edition) Blitzer 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 $g\left( x \right)=-\left| x-2 \right|$.