Question

Analyze the function f(x) = - tan 4x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes (6 points

Answer 1

Just a reminder on terms, domain are all valid x values, range are all possible y values
period is when the pattern repeats, and vertical asymptotes are where the function is undefined.

Answer 2

I know, I'm just not sure how to pull the necessary information from the function itself. But thank you!

Answer 3

ok tan(x) is periodic with a period of pi, since you have tan(4x) set 4x=pi so for your case the period will be pi/4.

Answer 4

vertical asymptotes of tan(x) occur at -pi/2 and pi/2 and also when you add pi to each, or in otherwords at pi/2 + n pi, so again set this equal to 4x to yield the retricemptotes occur at pi/8+npi/4

Answer 5

*asymptotes

Answer 6

tangent goes to positive and negative infinity in the y direction, and is defined in the x direction at everywhere but those asymptotes we mentioned.