Respuesta :
Given:
The function is:
[tex]f(x)=\sin x[/tex]
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
[tex]g(x)=kf(x)+b[/tex] .... (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:
[tex]g(x)=2f(x)+3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]k=2[/tex], it means the graph is vertically stretched by a factor of 2.
[tex]b=3[/tex], it means the graph is shifted up 3 units.
Therefore, the correct option is D.
