# How do you graph -2tan3(x - 30) + 1?

Jul 29, 2018

See graph and details.

#### Explanation:

$y = - 2 \tan \left(3 \left(x - \frac{\pi}{6}\right)\right) + 1$, asymptotic

$3 \left(x - \frac{\pi}{6}\right) \ne \left\{\left(2 k + 1\right) \frac{\pi}{2}\right\} , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

$\Rightarrow x \ne \left\{\left(2 k + 2\right) \frac{\pi}{6}\right\} = \left\{2 k \left(\frac{\pi}{6}\right)\right\} = \left\{k \left(\frac{\pi}{3}\right)\right\}$

The period = the period of $\tan 3 x = \frac{\pi}{3}$. See graph, with

asymptotes.
graph{(1/2(y-1)cos(3(x+pi/4))+sin(3(x+pi/4)))(x-1/3pi+0.0001y)(x+1/3pi+0.0001y)(x-2/3pi+0.0001y)(x+2/3pi+0.0001y)(x-pi+0.0001y)(x+pi+0.0001y)=0[ -4 4 -2 2]}