QuestionGraph the given function. State the period, amplitude, phase shift, and vertical shift of the function. $$y=-\sin \left(x+\frac{\pi}{6}\right)$$

Studdy Solution
Graph the function using the identified transformations:
1. Start with the basic sine curve.
2. Reflect the curve over the x-axis because of the negative amplitude.
3. Apply the phase shift by moving the curve $\frac{\pi}{6}$ units to the left.
4. The period remains $2\pi$, so ensure the graph completes one cycle over this interval.
5. No vertical shift is needed as $d = 0$.
The function $y = -\sin \left(x + \frac{\pi}{6}\right)$ has an amplitude of 1, a period of $2\pi$, a phase shift of $-\frac{\pi}{6}$ (left), and no vertical shift.