Graph f(x) = 3sin(2x + pi)
First we will consider the graphs of sin(x) (in black) and 3sin(x)(in red).
Here, we notice that the two graphs are the same, except for the fact that 3sin(x) has an amplitude thrice as large as sin(x). That translates to a vertical stretch by a factor of 3.
Now, we will graph 3sin(2x) (in blue) and compare it with the function 3sin(x) (in red):
Here, we notice that the two graphs are the same, except for the fact that 3sin(2x) has period equal to `(2pi)/2=pi.`
Finally, we will graph f(x)= `3sin(2x+pi)` (in green) and draw a comparison with the function 3sin(2x) (in blue):
We notice that this is the same graph as 3sin(2x), except that we have shifted every point to the left by `pi/2` .