Analyze the function f(x) = - tan 4x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes

Question

Analyze the function f(x) = - tan 4x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes

blurbendy · Answer

All I know is that the range is all real numbers.  sorry, been a while since I've done this stuff.

ganeshie8 · Answer

$$\large \rm   f(x) = -\tan(4x)$$

ganeshie8 · Answer

Say $\large \rm  4x= t$
$$\large \rm    f(t) = -\tan(t)$$

ganeshie8 · Answer

what do you know about domain of a normal `tan` function  ?

sleepyjess · Answer

all real numbers except when cos x = 0

sleepyjess · Answer

@ganeshie8

ganeshie8 · Answer

Vrey good. if we write $\large \tan (4x) = \dfrac{\sin (4x)}{\cos  (4x)}$

can we say the domain of $\tan(4x)$ is all real numbers except  when $\cos(4x) = 0$ ?

sleepyjess · Answer

how do i find the period?

ganeshie8 · Answer

whats the period of $\tan (t)$ ?

sleepyjess · Answer

$\pi/2$

ganeshie8 · Answer

nope, try again

sleepyjess · Answer

$\pi$?

ganeshie8 · Answer

yes, since $\tan (x)$ takes a time of $\pi$ seconds to complete one cycle, 
$\tan (4x)$ will take just $\large \dfrac{\pi}{4}$ seconds to complete one cycle

ganeshie8 · Answer

so the period of tan(4x) would be  pi/4

ganeshie8 · Answer

basically tan(4x) runs four times faster than tan(x), so its period(time) is also 4 times less

sleepyjess · Answer

would the asymptotes be $\pi/8~and~-\pi/8$?

ganeshie8 · Answer

Looks god!