Let's first graph `y = sin 2x` (without the "+ 1") to get an idea of what phase shift means.
The amplitude is 1 and the period is `(2π)/2 = π.`
I have drawn a little more than 2 cycles, starting from `x = 0`.
The graph of `y=sin(2x)` for `0 ≤ x ≤ 6.5`
Now let's consider the phase shift. Using the formula above, we will need to shift our curve by:
Phase shift `=-c/b=-1/2=-0.5`
This means we have to shift the curve to the left (because the phase shift is negative) by `0.5`. Here is the answer (in green). I have kept the original y = sin 2x (in dotted gray) so you can see what's happening.
The graph of `y=sin(2x+1)` for `-0.5 ≤ x ≤ 6.7`
Note that the curve passes through:
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