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

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 the tangent - type function, we can also find the period by observing the horizontal distance between two consecutive vertical asymptotes.

Step2: Identify consecutive vertical asymptotes

From the given graph, we can see that two consecutive vertical asymptotes are at $x = \frac{5\pi}{2}$ and $x=-\frac{5\pi}{2}$.

Step3: Calculate the period

The period $T$ is the difference between the $x$ - values of two consecutive vertical asymptotes. So, $T=\frac{5\pi}{2}-\left(-\frac{5\pi}{2}\right)$. [ \begin{align*} T&=\frac{5\pi}{2}+\frac{5\pi}{2}\ &=\frac{5\pi + 5\pi}{2}\ &=5\pi \end{align*} ]

Answer:

$5\pi$