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

1 Answer
Jul 19, 2018

#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 ]} .