Answer: OPTION A.
Step-by-step explanation:
Some tranformations for a function f(x):
If [tex]f(x)+k[/tex], then the function is shifted up "k" units.
If [tex]f(x)-k[/tex], then the function is shifted down "k" units.
If [tex]bf(x)[/tex], and [tex]b>1[/tex], then the function is vertically stretched by a factor of "b".
If [tex]bf(x)[/tex], and [tex]0<b<1[/tex], then the function is vertically compressed by a factor of "b".
If [tex]f(bx)[/tex], and [tex]b>1[/tex], then the function is horizontally compressed by a factor of [tex]\frac{1}{b}[/tex]
If [tex]f(bx)[/tex], and [tex]0<b<1[/tex], then the function is horizontally stretched by a factor of [tex]\frac{1}{b}[/tex]
Since the function f(x) is:
[tex]f(x)=\frac{1}{2}sin(x)+2[/tex]
And the function g(x) is:
[tex]g(x) = 2 sin (x) +8[/tex]
You can observe that the function g(x) is the function f(x) but shifted up 6 units and vertically stretched by a factor of 4.
