How do you find the domain, range, and asymptote for #y = 1 + cot ( 3x + pi/2 )#?

1 Answer
Nov 22, 2016

Answer:

Graph reveals all details. Noe that #pi=3.14#, nearly, See explanation, for numerical facts.

Explanation:

graph{y-1+tan( 3x)=0 [-10, 10, -5, 5]}

#y=1+cot(3x+pi/2)=1-tan 3x#

The period for the graph is #pi/3#. is

y is infinitely discontinuous at #x= k/6pi+pi/3), k = 0, +-1, +-2, +-3

The piecewise domain:

#x in (k/6pi, k/6pi+pi/3), k = 0, +-1, +-2, +-3, ..#.

Range: #y in (-oo, oo)#.+-3, ...#

As #x to (k/6pi, k/6pi+pi/3), k = 0, +-1, +-2, +-3, ...y to +-oo#

Asymptotes: #x=k/6pi+pi/3, k = 0, +-1, +-2, +-3, ...#

Have a look at the points inflexion aligned upon y =1,

wherein #x=.k/3pi, k = 0, +-1, +-2, +-3, ...#