The parent tangent function is to be examined on the interval

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

The parent tangent function

y=\tan x

is to be examined on the interval

(-\pi,\pi)

. (a) Determine all vertical asymptotes of the graph in this interval and write their equations. (b) Find the

x

–intercept(s) and state their coordinates. (c) Draw the graph of

y=\tan x

(-\pi,\pi)

, showing clearly each asymptote and the behaviour of the curve as it approaches them. (d) Using your graph in part (c), describe the range of

y=\tan x

and comment on the periodicity visible in the sketch.