The function given is \( f(x) = 2 \sin\left(x + \frac{\pi}{6}\right) \).
To find the phase shift, we need to use the standard form of the sine function, which is:
\[ f(x) = a \sin(b(x - c)) + d \]
where:
- \( a \) is the amplitude,
- \( b \) affects the period,
- \( c \) is the phase shift, and
- \( d \) is the vertical shift.
In this case, the equation is:
\[ f(x) = 2 \sin\left(1 \cdot \left(x + \frac{\pi}{6}\right)\right) \]
The phase shift \( c \) can be found by rewriting the argument of the sine function:
\[ x + \frac{\pi}{6} = x - \left(-\frac{\pi}{6}\right) \]
Thus, the phase shift is:
\[ c = -\frac{\pi}{6} \]
Therefore, the correct answer regarding the phase shift of the function is:
\[ -\frac{\pi}{6} \]
So, the response is:
−π6 (negative Start Fraction pi over 6 End Fraction)