What is the domain of y=tan^3(x) +3?

Jul 29, 2018

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

Explanation:

The period of $y = a {\tan}^{n} \left(b x + c\right) + d , n = 1 , 2 , 3 , \ldots$ is $\frac{\pi}{\left\mid b \right\mid}$ #.

The asymptotes are given by

$b x + c = \left(2 k + 1\right) \frac{\pi}{2} \Rightarrow x = \frac{1}{b} \left(\left(2 k + 1\right) \frac{\pi}{2} - c\right) ,$

$k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

So,

the period of $y = {\tan}^{3} x + 3 : \pi$

The asymptotes: $x = \left(2 k + 1\right) \frac{\pi}{2} , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

$\Rightarrow$ the domain is given by

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

See graph, with asymptotes.
graph{(y - (tan(x ))^3 - 3 )(x-1/2pi+0.001y)=0}