Graphing Cotangent with a Phase Shift and Vertical Translation

The video tutorial explains how to graph the cotangent function y = 2 cotangent(X - π/2) - 1. It covers determining the period, identifying critical points like intercepts and asymptotes, and understanding transformations such as phase shifts and vertical translations. The tutorial provides a step-by-step guide to graphing the function, highlighting the effects of transformations on the graph's shape and position.

What is the initial period of the cotangent graph when B is 1?

• π

• 3π/2

• π/2

• 2π

Which of the following are considered critical points in the cotangent graph?

• Y-intercepts and peaks

• Asymptotes and troughs

• X-intercepts and asymptotes

• Peaks and troughs

How does a negative vertical translation affect the cotangent graph?

• Shifts the graph up

• Shifts the graph down

• Stretches the graph horizontally

• Compresses the graph vertically

What effect does a coefficient greater than one have on the cotangent graph?

• Vertically compresses the graph

• Vertically stretches the graph

• Horizontally stretches the graph

• Horizontally compresses the graph

Where does the initial period of the cotangent graph start and end after a phase shift of π/2?

• 0 to π

• π/2 to 3π/2

• π to 2π

• 3π/2 to 5π/2

What is the result of a vertical compression on the cotangent graph?

• The graph becomes narrower

• The graph becomes wider

• The graph shifts upwards

• The graph shifts downwards

How does the graph of the cotangent function change with a phase shift?

• It moves left or right

• It becomes narrower

• It becomes wider

• It moves up or down