Question

Can someone check if this is correct?


Analyze the function f(x) = - tan 4x. Include:

- Domain and range
- Period
- Two Vertical Asymptotes

Alright so I first know that

Period is: pi/b = pi/4

Answer 1

I've seen the mistake for VA I believe.

retricemptote is:

pi/2 quotient 4 = pi/8
3pi/2 quotient 4 = 3pi/8

Can anyone help me with this?

Answer 2

I meant to say asyymptote

Answer 3

Hmmm; I believe I can just put

Range: All real numbers

Domain: All Real numbers except multiple of pi/2?

Answer 4

Hmm I think you were on the right track before,
The asymptotes are at pi/8, 3pi/8, 5pi/8, ...

So we could simplify their location by saying, \(\large \dfrac{\pi}{8}\pm\dfrac{\pi}{2}k\)

Answer 5

So the domain would be .. yah the way you were thinking, all reals except .. those asymptotes, the fancy way we wrote it out.

Answer 6

It might look a little nicer if we wrote it in set notation, but no big deal,
\[\large D=\left\{ x \;|\; x\ne \frac{\pi}{8}\pm\frac{\pi}{2}k \right\}\]
This translates to,
"The Domain D is the set of all points x, such that x does not equal ..that "

Answer 7

Awesome! I'm going to give you the best responce, but I just have one question (forgive me, my teacher teaches me ABSOLUTELY nothing). What would I put for the D then,

Domain is all numbers except multitude of pi/2, is that correct?

Answer 8

Bahh I did that wrong.
My bad.

There should be one asymptote popping up every `period`.
You correctly identified asymptotes at \(\large \dfrac{\pi}{8}\) and \(\large \dfrac{3\pi}{8}\).

Notice that those are \(\large \dfrac{\pi}{4}\) away from each other?
A new asymptote will pop up every \(\large \dfrac{\pi}{4}\), which is our period.


It's kind of hard to say it the way you're trying to, in words,
We're starting at pi/8, and then adding or subtracting any multiples of pi/4 to reach the other asymptotes.

The Domain is All Reals except \(\large \dfrac{\pi}{8}\pm\dfrac{\pi}{4}k\).
The k is any integer value. This ^ ugly expression is the location of each asymptote.
The domain is all reals except those locations.

I'm sorry, I can't think of an easier way to explain that lol.