Question

What effect does changing the function f(x)=1/2 sin(x)+2 to the function g(x)= 2 sin(x)+8 have on the graph of f(x)?

The graph is vertically stretched by a factor of 4 and shifted up 6 units.

The graph is horizontally stretched by a factor of 6 and shifted up 4 units.

The graph is vertically stretched by a factor of 6 and shifted up 4 units.

The graph is horizontally stretched by a factor of 4 and shifted up 6 units.

Answer 1

g(x) = 4f(x)

The graph is vertically stretched by a factor of 4.

None of the offered choices is correct.

_____
Whoever wrote your answer key probably claims the first choice to be correct. It is not correct. If you were to compute g(x) = 4*f(x) +6, you would get
.. g(x) = 2sin(x) +14
which is not the g(x) that is part of the problem statement.