Question

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

Thanks so much for your help

Answer 1

\[Domain { x \in \mathbb{R} : \neq \pi/8 \pm 2\pi/8}\]\[Range { y \in \mathbb{R} }\]
You can get the Period from the Domain and the Vertical asymptotes there too.

Answer 2

I'm sorry could you please explain to me how you got the answer? I'm really trying to learn this stuff I'm just having a tough time. Thanks for answering!

Answer 3

Graph the function (as can be seen here: http://www.wolframalpha.com/input/?i=f%28x%29+%3D+-+tan+4x) The domain is everything x can be, which is all real numbers, except for -pi/8, pi/8, 3pi/8 (as those are the ends of the periods). The ends of the periods are also the vertical asymptotes. As for the range, y can be any number because it continues upward infinitely.

Answer 4

So the domain and range the same in this case?

Answer 5

No, the Domain and Range are different because the domain has asymptotes whilst the range, as Ash has said, can be anything

Answer 6

So there is no way to narrow down the range in this case? You can say the range is all real numbers?

Answer 7

yup!

Answer 8

thanks man

Answer 9

no probs =D

Answer 10

Yeah thanks. So the vertical asymptotes are +- pi/8 and 3pi/8?

Answer 11

Hmm, just -pi/8 and 3pi/8.

Answer 12

+/- 2pi/8 as well

Answer 13

where is the period and the two vertical asymptotes ?