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.

Answer 1

It is the graph shifted 6 units right

Answer 2

General Idea:

The function translation / transformation rules are given below:

f (x) + k shifts the function k units upward.

f (x) – k shifts the function k units downward.

f (x + h) shifts the function h units to the left.

f (x – h) shifts the function h units to the right.

–f (x) reflects the function in the x-axis (that is, upside-down).

f (–x) reflects the function in the y-axis (that is, swapping the left and right sides).

Applying the concept:

If y = f(x), then y = csc(x – 6) can be represented as y = f(x-6).

Conclusion:

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