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

Jul 30, 2016

Period is $\frac{\pi}{2}$. Within every period, at $x = \pm \frac{\pi}{4} , \pm \frac{5 \pi}{4} , \pm \frac{9 \pi}{4} , \ldots , \tan 2 x \to \pm \infty$. So, amplitude cannot be specified as an absolute maximum..

#### Explanation:

The period of tan (kx) is $\frac{\pi}{k}$.

Here k = 2, and so, the period is $\frac{\pi}{2}$.

See how it works.

f(x)=3 tan 2x + 4

$f \left(x + \frac{\pi}{2}\right)$

$= 3 \tan \left(2 \left(x + \frac{\pi}{2}\right)\right) + 4$

$= 3 \tan \left(2 x + \pi\right) + 4$

$= 3 \tan 2 x + 4$

$= f \left(x\right)$

Within every period,

at discontinuities $x = \pm \frac{\pi}{4} , \pm \frac{5 \pi}{4} , \pm \frac{9 \pi}{4} , \ldots , \tan 2 x \to \pm \infty$.

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

tan oscillations are unreal,, and so, virtual.