Question

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Answer 1

Well for the asymptotes look at the unit circle might help to memorize it

remember the identity

tan(x) = sin(x)/cos(x)

so you will have an asymptote everytime cos(x) = 0, because you cannot divide by zero

tan(4x) = sin(4x)/cos(4x)

these asymptotes will continue infinitely so you have to denote that in your answer

Answer 2

You will have vertical asymptotes as you approach where cos(x) = 0
this will also tell you what your domain is

Answer 3

as for range of tan(x), look at the graph of the function and memorize it. It helps to know it. from the graph of tan(x) you can see what the range of tan(4x) is.

Answer 4

okay thank you! Do you know how to find the period?

Answer 5

as for period all you do is divide 2pi by the multiple or divider of x or theta in the function.

so if you had

sin(3x)

to find the period

2pi/3x

to find the period of

sin(x/4)

2pi/(1/4)
=
2pi(4/1)
=
2pi(4)

Answer 6

But yeah if you plan on taking calculus in university memorize these trig graphs and if you feel like you want to be super prepared you can memorize the unit circle but there are other better ways to remember it apparently

Answer 7

made a mistake

to find the period sin(3x)
2pi/3

Answer 8

it is pretty simple hope you follow

Answer 9

follow?

Answer 10

so would the domain be all real numbers except npi/8 where n is odd
range all real numbers
and asymptotes pi/8 +- n4/pi?

Answer 11

well you only have to denote two asymptotes for this function, so dont worry about showing then repeated, range =all real numbers like you said

as for domain it would be the period +/- npi , where n = an integer

Answer 12

what would the period be again? +/- npi?

Answer 13

I showed you how to figure out period

Answer 14

would it be 2pi/3x?

Answer 15

ugh no,

just divide 2pi by the multiple or divider of x in the trig function

so sin(3x)

would have the period
2pi/3


cos(x/3)

would have the period

2pi/(1/3)

etc

Answer 16

alright thank you