Question

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

Answer 1

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.