Question

Graphing: y= cot(theta -(PI/4))

Answer 1

Refer to the attached plot.

Answer 2

\[cotx=\frac{ cosx }{ sinx }\]
, so the zeros of cosine are the zeros of the graph, and the zeros of sine are the asymptotes.

Answer 3

The domain and range?

Answer 4

The asymptotes made by the zeros of the sine function make the graph discontinuous, so for the parent function y = cotx, the domain would be
x≠πn
, where n is any integer.
This is because sin(pi) = 0.
However, there is a horizontal shift (phase shift) pi/4 to the right.
So the asymptote is now pi/4, so add π/4.
x≠(π/4) + πn

Answer 5

The range is \[(-\infty, \infty)\] as you can see in the graphs above.