question determine the period of the following tangent graph. if necessary, write your answer as a fraction…

Explanation:

Step1: Recall period - formula for tangent function

The general form of the tangent function is $y = A\tan(Bx - C)+D$, and its period is given by $T=\frac{\pi}{|B|}$. For the standard tangent function $y = \tan(x)$, the period is $\pi$. When looking at the graph of a tangent - type function, we can also find the period by identifying the horizontal distance between two consecutive vertical asymptotes.

Step2: Identify vertical asymptotes on the graph

From the given graph, we can see that two consecutive vertical asymptotes are at $x =-\frac{\pi}{9}$ and $x=\frac{8\pi}{9}$.

Step3: Calculate the period

The period $T$ is the difference between the $x$ - values of two consecutive vertical asymptotes. So, $T=\frac{8\pi}{9}-\left(-\frac{\pi}{9}\right)$. $T=\frac{8\pi + \pi}{9}=\frac{9\pi}{9}=\pi$.

Answer:

$\pi$