Question

how is the graph of y = csc(x − 6) transformed from its parent function?
○ it is the graph of y = csc(x) shifted 6 units up.
○ it is the graph of y = csc(x) shifted 6 units right.
○ it is the graph of y = csc(x) shifted 6 units left.
○ it is the graph of y = csc(x) shifted 6 units down.

Explanation:

Step1: Recall Transformations

For a function \( y = f(x - h) \), the graph is shifted \( h \) units right if \( h>0 \), left if \( h<0 \). For \( y = \csc(x - 6) \), compare to \( y=\csc(x) \) (parent function). Here, \( h = 6>0 \).

Step2: Determine Shift Direction

Since \( h = 6 \) in \( y = \csc(x - 6) \) (form \( y = f(x - h) \)), the graph shifts 6 units right.

Answer:

B. It is the graph of \( y = \csc(x) \) shifted 6 units right.