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 transformation rules

For a function \( y = f(x - h) \), the graph of \( y = f(x) \) is shifted \( h \) units to the right if \( h>0 \), and to the left if \( h < 0 \). For vertical shifts, the form is \( y=f(x)+k \), shifted up \( k \) units if \( k > 0 \), down if \( k<0 \).

Step2: Analyze given function

The given function is \( y=\csc(x - 6) \), where \( f(x)=\csc(x) \) and \( h = 6 \) (since the form is \( f(x - h) \) with \( h = 6>0 \)). So according to the horizontal shift rule, the graph of \( y = \csc(x) \) is shifted 6 units to the right.

Answer:

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