use transformations to solve ;

Question

anonymous · Answer

$$\large y=-2f (\frac{ 1 }{ 2 } x) +3$$

anonymous · Answer

attachment

anonymous · Answer

can someone explain ?

anonymous · Answer

What I think :
$$g(x)=-2f(\frac{ 1 }{ 2 }x) +3$$
If you evaluate for x=4,
$$g(4)=-2f(2)+3$$
by looking at the graph, you see that f(2) = 0
thus,
$$g(4)=3$$

anonymous · Answer

hmm okay

anonymous · Answer

I'm not sure what they mean by "use transformations"

anonymous · Answer

they mean like apply all the changes to the graph looking at the formula above
like the (-) means it's reflect on the x axis, but i dont understand the rest

anonymous · Answer

You'd have to draw a second graph of $$y_{g}=g(x)$$, using the formula and the graph $$y_{f}=(\frac{ 1 }{ 2 }x)$$

anonymous · Answer

$$y _{g}=-2y _{f}+3$$
$$y _{f}$$ is found by looking at the first graph, at a value on the x-axis that is x/2