Question

Sketch the graph of y=-2g(x)+2 given the graph of g in the figure.

Answer 1

On the graph of g(x), we have these three points:

`\begin{gathered} (-4,-1) \\ (-1,-1) \\ (2,1) \end{gathered}`

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

`\begin{gathered} \implies y=-2g(x)+2=-2(-1)+2=2+2=4 \\ \implies(-4,4) \end{gathered}`

At x=-1, g(x)=-1

`\begin{gathered} \implies y=-2g(x)+2=-2(-1)+2=2+2=4 \\ \implies(-1,4) \end{gathered}`

At x=2, g(x)=1

`\begin{gathered} \implies y=-2g(x)+2=-2(1)+2=-2+2=0 \\ \implies(2,0) \end{gathered}`

Next, plot these new points (-4,4), (-1,4), and (2,0) on the graph as shown below.