the periodic function f has a period of π. which of the following could define f(x)? a tan(1/2 x) b tan x c…

Explanation:

Step1: Recall period - formula for tangent function

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

Step2: Check option A

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

Step3: Check option B

For $y=\tan(x)$, $B = 1$. Then $T=\frac{\pi}{|1|}=\pi$.

Step4: Check option C

For $y=\tan(2x)$, $B = 2$. Then $T=\frac{\pi}{|2|}=\frac{\pi}{2}$.

Step5: Check option D

For $y=\tan(\pi x)$, $B=\pi$. Then $T=\frac{\pi}{|\pi|}=1$.

Answer:

B. $\tan x$