which is an x - intercept of the graph of the function y = cot(3x)?\n(π/6,0)\n(π/3,0)\n(3π,0)\n(6π,0)

Explanation:

Step1: Recall cotangent - zero condition

The cotangent function (y = \cot(u)) is zero when (u=(2n + 1)\frac{\pi}{2}), (n\in\mathbb{Z}). Here (u = 3x), so we set (3x=(2n + 1)\frac{\pi}{2}).

Step2: Solve for (x)

[x=\frac{(2n + 1)\pi}{6}]

Step3: Find an (x) - intercept

When (n = 0), (x=\frac{\pi}{6}). The (x) - intercept is of the form ((x,0)), so one (x) - intercept is ((\frac{\pi}{6},0)).

Answer:

A. ((\frac{\pi}{6},0))