Question

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)?

Answer 1

Answer: OPTION A.

Step-by-step explanation:

Some tranformations for a function f(x):

If $f(x)+k$, then the function is shifted up "k" units.

If $f(x)-k$, then the function is shifted down "k" units.

If $bf(x)$, and $b>1$, then the function is vertically stretched by a factor of "b".

If $bf(x)$, and $0$, then the function is vertically compressed by a factor of "b".

If $f(bx)$, and $b>1$, then the function is horizontally compressed by a factor  of $\frac{1}{b}$

If $f(bx)$, and $0$, then the function is horizontally stretched by a factor  of $\frac{1}{b}$

Since the function f(x) is:

$f(x)=\frac{1}{2}sin(x)+2$

And the function g(x) is:

$g(x) = 2 sin (x) +8$

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.