What is the domain of #y=tan^3(x) +3#?

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Answer 1 · 2018-07-29T14:30:08

Domain: # x ne ( 2k+ 1 ) pi/2, k = 0, +-1, +-2, +-3,...#

The period of #y = a tan^n(b x + c ) + d, n = 1, 2, 3, ...# is #pi/abs b# #.

The asymptotes are given by

#b x + c = ( 2 k + 1 ) pi/2 rArr x = 1/b ( ( 2 k + 1 ) pi/2 - c),#

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

So,

the period of # y = tan^3x + 3: pi#

The asymptotes: #x = ( 2k+ 1 ) pi/2, k = 0, +-1, +-2, +-3,...#

#rArr# the domain is given by

# x ne ( 2k+ 1 ) pi/2, k = 0, +-1, +-2, +-3,...#

See graph, with asymptotes.
graph{(y - (tan(x ))^3 - 3 )(x-1/2pi+0.001y)=0}