how do i solve this

Question

the graph of y=2sin(3x+π/4) is obtained from the graph of y=2sin(3x) by shifting to

 

1.) to the left π/12 units

 

2.) to the right π/12 units.

 

3.) to the left π/8 units.

 

4.) to the right π/8 units.

 

5.) to the left π/4 units

 

6.) to the right π/4 units

Answer 1

The graph of y=2sin(3x+π/4) is obtained from the graph of y=2sin(3x) by shifting to _____.

 

3x → 3x + pi/4 = 3(x + pi/12) = 3(x - (-pi/12))

 

So this is a shift to the left by pi/12.

 

NB: To translate the graph of an equation by h in the x direction and k in the y direction, i.e., a translation vector of <h,k>, change x to x-h and y to y-k.