# How do you graph  y=5-tan2(x-pi)?

Aug 14, 2018

See explanation and graph.

#### Explanation:

y = 5 - tan ( 2 ( x - pi ) = 5 + tan ( 2pi - 2x ) = 5 - tan 2x,

$2 x \ne$ ( asymptotic zero of cos 2x ) ( 2k + 1 ) pi/2#

$\Rightarrow x \ne \left(2 k + 1\right) \frac{\pi}{4} , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

The period = $\pi$/2.

Amplitude of $\infty$-arm wave is 1/2( period ) = $\frac{\pi}{4}$

Vertical shift is 5 $\Rightarrow$ axis is y = 5.

See graph, depicting all these aspects.
graph{(y-5+tan (2x))(y-5)(x-pi/4+0.01+0.005y)(x+pi/4--0.05+.005y)=0[-6 6 0 10]}