Question

use transformations to solve ;

Answer 1

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

Answer 2

can someone explain ?

Answer 3

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,
\[g(4)=3\]

Answer 4

hmm okay

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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