Question

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

Answer 1

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.