Question

the the graph function of f is shown on the coordinate plane graph the line representing the function of g if g is defined as shown below

Answer 1

the translation x+2 moves the graph 2 units to the left, and the multiplication -1/2 changes the slope. Now, we can obtain the equation of f by looking at the graph, since the slope is 2 and the y-intercept is -6, then

$f(x)=2x-6$

Then,

$\begin{gathered} g(x)\text{ = -}\frac{1}{2}f(x+2) \\ g(x)=-\frac{1}{2}(2(x+2)-6) \\ g(x)=-\frac{1}{2}(2x-2) \\ g(x)=-x+1 \end{gathered}$