The blue curve is graph of y = tan x. The blue curve is never across the red line. The red line is the asymptotes of y = tan x. Now, we will find the equation of the red lines.

pi/2 = pi/2 + 0 × pi

3pi/2 = pi/2 + 1 × pi

5pi/2 = pi/2 + 2 × pi

-pi/2 = pi/2 + (-1) × pi

So, the red lines have the equation: x = pi/2 + k pi, in which k = 0, +-1, +-2,...

Because the blue curve is never across the red line, so, the domain of the function y = tan x is x not equal to pi/2 + k pi, k is an integer.

The minimum period of y = tan x is: minimum period T = pi

Because the blue curve is symmetry to the origin, so, the function y = tan x is an odd function.