Question

If the parent function y= csc x goes through a transformation to produce 1+csc (x-π), what is the resultant shift in the function’s graph?

Answer 1

The transformations which have made to produce the function
y₂ = 1+csc (x-π) from the parent function y = csc x
1. shift up one unit ⇒ shift one unit in the direction of positive y
2. shift to the left equal to π ⇒ shift π units in the direction of positive x

See the attached figure.
Blue graph represents the parent function
Red graph represents the produced function after transformation.