1.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)?
a. the graph is horizontally stretched by a factor of 4 and shifted up 6 units.
b. the graph is vertically stretched by a factor of 4 and shifted up 6 units
c. the graph is vertically stretched by a factor of 6 and shifted up 4 units.
d. the graph is horizontally stretched by a factor of 6 and shifted up 4 units.

OPTION A.

Step-by-step explanation:

Some tranformations for a function f(x):

If , then the function is shifted up "k" units.

If , then the function is shifted down "k" units.

If , and , then the function is vertically stretched by a factor of "b".

If , and , then the function is vertically compressed by a factor of "b".

If , and , then the function is horizontally compressed by a factor  of

If , and , then the function is horizontally stretched by a factor  of

Since the function f(x) is:

And the function g(x) is:

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.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a