How do you use the amplitude and period to graph #3tan2x+4#?

1 Answer
A. S. Adikesavan
Jul 30, 2016

Period is #pi/2#. Within every period, at #x =+-pi/4, +-(5pi)/4, +-(9pi)/4, ..., tan 2x to +-oo#. So, amplitude cannot be specified as an absolute maximum..

Explanation:

The period of tan (kx) is #pi/k#.

Here k = 2, and so, the period is #pi/2#.

See how it works.

f(x)=3 tan 2x + 4

#f( x + pi/2 )#

#=3 tan (2(x+pi/2))+4#

#=3 tan (2x+pi)+4#

#=3tan 2x + 4#

#=f(x)#

Within every period,

at discontinuities #x =+-pi/4, +-(5pi)/4, +-(9pi)/4, ..., tan 2x to +-oo#.

So, amplitude (absolute periodic maximum) cannot be specified.

tan oscillations are unreal,, and so, virtual.

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