Mathematics

Problem

For the function

y=\tan x

answer the following questions. a. (i) Determine all vertical asymptotes of the graph in the interval

\left[-\dfrac{3\pi}{2},\,\dfrac{5\pi}{2}\right]

. b. (ii) Sketch a rough graph of

y=\tan x

over the same interval, clearly marking each vertical asymptote and every

x

-intercept. c. (iii) From your sketch, state how many times the graph crosses the

x

-axis in this interval and justify your answer.