Describe how the graph of the function f(x)=sin(x−π6) differs from the graph of sinx .(1 point) Responses It shifts the graph of sinx to the right by π6 units. It shifts the graph of sine x to the right by Start Fraction pi over 6 End Fraction units. It shifts the graph of sinx up by π6 units. It shifts the graph of sine x up by Start Fraction pi over 6 End Fraction units. It shifts the graph of sinx down by π6 units. It shifts the graph of sine x down by Start Fraction pi over 6 End Fraction units. It shifts the graph of sinx to the left by π6 units.

Answer 1

The function \( f(x) = \sin\left(x - \frac{\pi}{6}\right) \) represents a horizontal shift of the function \( \sin(x) \). The transformation inside the sine function indicates that the graph is shifted to the right by \( \frac{\pi}{6} \) units.

Therefore, the correct response is:

It shifts the graph of \( \sin(x) \) to the right by \( \frac{\pi}{6} \) units.