Question

The function f(x)= cot(3x-pi/2) has ___.?

A. period pi/3 and asymptote at x=pi/6
B. period 2pi/3 and asymptote at x=pi/6
C. period 2pi/3 and asymptote at x=0
D. period pi/3 and asymptote at x=0

Answer 1

the period of the general cotangent function shown below is T = pi/B

y = A*cot(Bx - C) + D

Answer 2

let me know if that's enough to get you started

Answer 3

I still don't quiet understand

Answer 4

do you see how the Bx and 3x match up?

Answer 5

yeah

Answer 6

so B = 3 and you plug that into T = pi/B to get pi/3 as the period

Answer 7

oh okay. And then how would I find the asymptote ?

Answer 8

what happens when you plug in x = 0 ?

Answer 9

you get 0?

Answer 10

yes, so because x = 0 produces a single number as an output, this means x = 0 is NOT a vertical asymptote

Answer 11

that leaves x = pi/6 to be an asymptote

sure enough if you plug in x = pi/6, you should get NAN or UND or whatever error your calculator will spit out

Answer 12

so it's not D?

Answer 13

it's A actually

Answer 14

yeah D is out because f(0) is defined

Answer 15

Okay i understand thank you so much:)

Answer 16

glad to be of help