Question

Find the domain, range and two vertical asymptotes of the following function:f(x) = - 2 cot 3x

Answer 1

cot(3x) = cos(3x)/sin(3x)

Answer 2

the denominator cannot be zero, if it were then

sin(3x) = 0

3x = arcsin(0)

3x = pi*n ... n is any integer

x = (pi/3)*n

Answer 3

this means that domain is basically the set of all real numbers...but...you must kick out values of the form x = (pi/3)*n, n is any integer, to avoid division by zero

Answer 4

also, this means that the vertical asymptotes are

x = (pi/3)*n

or

x = pi/3, x = 2pi/3, x = pi, etc etc

Answer 5

with tangent and cotangent, the range is always the set of real numbers

so that applies to -2*cot(3x) as well

Answer 6

Thank you! c:

Answer 7

you're welcome