the periodic function g has a period of 3π. which of the following could define g(x)?\no tan(x/3)\no…

Answer:

A. $\tan\left(\frac{x}{3}\right)$

Explanation:

Step1: Recall tangent - period formula

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

Step2: Test each option

For $y = \tan\left(\frac{x}{3}\right)$, $B=\frac{1}{3}$, and $T=\frac{\pi}{\left|\frac{1}{3}\right|}=3\pi$. For $y=\tan(3x)$, $B = 3$, and $T=\frac{\pi}{|3|}=\frac{\pi}{3}$. For $y=\tan\left(\frac{x}{3\pi}\right)$, $B=\frac{1}{3\pi}$, and $T=\frac{\pi}{\left|\frac{1}{3\pi}\right|}=3\pi^{2}$. For $y=\tan(3\pi x)$, $B = 3\pi$, and $T=\frac{\pi}{|3\pi|}=\frac{1}{3}$.