Question

How do you graph `y=3tan(2pit)` over the interval `[-1/2, 1/2]`?

Answer 1

`y = 3 tan 2pix`.

The period for this graph is `pi/(2pi) = 1/2`

The asymptotes are `2pix = (( 2k + 1 )(pi/2) rArr x = ( 2k + 1 )/4`

k = 0, +-1, +-2, +-3, ...#

So, the graph for`x in [ - 1/2, 1/2 ]` is for

`x in [ -1/2, -1/4 ) U ( -1/4, 1/4) U ( 1/4, 1/2 ]`, excluding infinite

discontinuities at `x = +- 1/4`.

Now see graph.
graph{y-3 tan ( 2 pi x )=0[-0.5 0.5 ]} .