Describe how the graph of the function \( f(x)=\sin \left(x-\frac{\pi}{6}\right) \) differs from the graph of \( \sin x \) (1 point) It shifts the graph of \( \sin x \) to the right by \( \frac{\pi}{6} \) units. It shifts the graph of \( \sin x \) up by \( \frac{\pi}{6} \) units. It shifts the graph of \( \sin x \) down by \( \frac{\pi}{6} \) units.

The graph of the function \( f(x)=\sin \left(x-\frac{\pi}{6}\right) \) represents a horizontal shift of the standard sine function. Specifically, it moves to the right by \( \frac{\pi}{6} \) units. This means that each point on the sine curve is displaced to the right, resulting in the original sine wave becoming "later" in phases without changing its shape or amplitude! If you're sketching this out, remember that the critical points, like the peaks and zero crossings, will also move accordingly. For instance, where \( \sin x \) typically reaches its maximum at \( \frac{\pi}{2} \), \( f(x) \) will peak at \( \frac{\pi}{2} + \frac{\pi}{6} = \frac{2\pi}{3} \). Just keep an eye on those phase adjustments and your graph will sing!