Functions can be transformed the same way as points or figures in the coordinate system.
If you add a determined value "d" to a function, it translates into a vertical translation upwards d units.
If you subtract "d" to a function, it translates into a vertical translation downwards d units.
[tex]f(x)\to g(x)=\frac{1}{2}f(x)+4[/tex]In this case, given the function
[tex]f(x)=x[/tex]If you add 4 units to the function, the function will move "up" 4 units.
As mentioned, this is a translation, the form of the functions are not changed, just their positions in the coordinate plane and the lines will be parallel.
Next, the function f(x)is multiplied by 1/2.
The transformation is a dilation.
Given a scale factor "a"
If |a|>0, the result is a vertical stretch, the line becomes steeper.
If |a|<0, the result is a vertical compression, the line becomes less steep.
So f(x) was compressed 1/2 and moved 4 units up.
The correct option is C.
