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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.

1 Answer

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Answer: OPTION A.

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<b<1, 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
(1)/(b)

If
f(bx), and
0<b<1, then the function is horizontally stretched by a factor of
(1)/(b)

Since the function f(x) is:


f(x)=(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.

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