On the graph of g(x), we have these three points:
[tex]\begin{gathered} (-4,-1) \\ (-1,-1) \\ (2,1) \end{gathered}[/tex]
We are required to sketch the graph of y=-2g(x)+2.
First, find the new coordinates using the given transformation.
At x=-4, g(x)=-1
[tex]\begin{gathered} \implies y=-2g(x)+2=-2(-1)+2=2+2=4 \\ \implies(-4,4) \end{gathered}[/tex]
At x=-1, g(x)=-1
[tex]\begin{gathered} \implies y=-2g(x)+2=-2(-1)+2=2+2=4 \\ \implies(-1,4) \end{gathered}[/tex]
At x=2, g(x)=1
[tex]\begin{gathered} \implies y=-2g(x)+2=-2(1)+2=-2+2=0 \\ \implies(2,0) \end{gathered}[/tex]
Next, plot these new points (-4,4), (-1,4), and (2,0) on the graph as shown below.
