Question

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.

Answer 1

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

Explanation:

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Answer 2

Given:

The function is:

`f(x)=\sin x`

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

`g(x)=kf(x)+b` .... (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:

`g(x)=2f(x)+3` ...(ii)

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

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

`b=3`, it means the graph is shifted up 3 units.

Therefore, the correct option is D.