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)?

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.

Answer 1

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.