1. what is the period of the function given? 2. which of the following is the function of the graph?

Explanation:

Step1: Recall period - definition

The period of a periodic function is the horizontal distance between two consecutive repeating parts of the graph.

Step2: Analyze the graph

For the given graph, we can see that the function repeats itself every (2\pi) units along the x - axis.

Answer:

(2\pi)

Since we don't have the options for the second - part "Which of the following is the function of the graph?", we can't answer that part. But if we assume it's a tangent - like function (due to the vertical asymptotes and the shape), a general form of a tangent function is (y = A\tan(Bx - C)+D), and for the basic tangent function (y=\tan(x)), the period is (\pi). However, from the graph, the period is (2\pi). If we consider a transformation of the form (y = \tan\left(\frac{1}{2}x\right)), its period (T=\frac{\pi}{\left|\frac{1}{2}\right|}=2\pi).