(tangent function transformations lc)\nthe function f(x)=tan(x/6). determine the period of f.

Answer:

$6\pi$

Explanation:

Step1: Recall tangent - period formula

The period of the tangent function $y = A\tan(Bx - C)+D$ is $T=\frac{\pi}{|B|}$.

Step2: Identify the value of B

For the function $f(x)=\tan(\frac{x}{6})$, we have $B = \frac{1}{6}$.

Step3: Calculate the period

$T=\frac{\pi}{\left|\frac{1}{6}\right|}=6\pi$.