The function f(x) is multiplied by a factor of 2 and then 3 is added to the function. f(x) = sin(x)
What effect does this have on the graph of the function?

A.) The graph is vertically compressed by a factor of 3 and shifted up 2 units.
B.) The graph is vertically stretched by a factor of 3 and shifted up 2 units.
C.) The graph is vertically compressed by a factor of 2 and shifted up 3 units.
D.) The graph is vertically stretched by a factor of 2 and shifted up 3 units.

Given:

The function is:

The function f(x) is multiplied by a factor of 2 and then 3 is added to the function.

To find:

The effect on the graph of the function.

Solution:

The transformation is defined as

               .... (i)

Where, k is stretch factor and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.  

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

It is given that the function f(x) is multiplied by a factor of 2 and then 3 is added to the function. So, the new function is:

            ...(ii)

On comparing (i) and (ii), we get

, it means the graph is vertically stretched by a factor of 2.

, it means the graph is shifted up 3 units.

Therefore, the correct option is D.

answer: x= -2y

step-by-step explanation:

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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