Question

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

Answer 1

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, ...`