Question

The parent cosecant function is shifted 2 units down, and its period is changed to 6pi. Which of the following is the graph of the transformed function?

Answer 1

Answer:

The parent secant function is sec(x).  

parent secant function period = 2π.

Two transformations are applied to this function.

1st Transformation:

The function is shifted down by 2 units. The resultant function will be:

sec(x) - 2

2nd Transformation:  

π  is the changed  period of the function

Both transformations after the resultant function will be :

sec(2x) - 2

The graph of a transformed function over 1 period is attached below.