Understanding Cosecant Function Transformations

The video tutorial explains how to describe and graph the transformation of the function y = 3csc(2x - π) - 2. It covers the identification of key parameters such as amplitude, period, phase shift, and vertical shift. The tutorial emphasizes the relationship between the sine and cosecant functions, demonstrating how to graph the sine function first and then use it to graph the cosecant function by identifying vertical asymptotes and points of concavity. The process involves sketching the midline, determining maximum and minimum values, and dividing the period into sub-intervals for accurate graphing.

What is the value of 'a' in the function y = 3csc(2x - π) - 2?

• 1

• 2

• 3

• 4

How is the period of the function y = 3csc(2x - π) - 2 calculated?

• 2π divided by a

• 2π divided by b

• π divided by d

• π divided by c

What is the phase shift of the function y = 3csc(2x - π) - 2?

• Left π units

• Right π/2 units

• Left π/2 units

• Right π units

What is the vertical shift of the function y = 3csc(2x - π) - 2?

• Down 2 units

• Up 3 units

• Down 3 units

• Up 2 units

Why is it helpful to graph the sine function when graphing the cosecant function?

• Because they are reciprocals

• Because they have the same period

• Because they have the same phase shift

• Because they have the same amplitude

What is the midline of the sine function corresponding to y = 3csc(2x - π) - 2?

• y = 0

• y = 1

• y = -1

• y = -2

What is the maximum value of the sine function corresponding to y = 3csc(2x - π) - 2?

• 4

• 3

• 2

• 1

Where do vertical asymptotes occur in the graph of the cosecant function?

• At the maximum points of the sine function

• At the minimum points of the sine function

• At the endpoints of the period

• At the midline of the sine function

How does the concavity of the sine function affect the cosecant function?

• Concave up sine results in concave down cosecant

• Concave down sine results in concave down cosecant

• Concave up sine results in concave up cosecant

• Concave down sine results in concave up cosecant

What is the final step in graphing the cosecant function?

• Drawing vertical asymptotes

• Highlighting the graph

• Plotting the sine function

• Identifying maximum and minimum points