Understanding Transformations of Cotangent Functions

The video tutorial explains how to describe and graph transformations of the cotangent function. It covers the effects of coefficients on the period and vertical stretch of the function. The period is calculated as 4π radians due to the coefficient of 1/4, and the graph is vertically stretched by a factor of 2. The tutorial demonstrates how to graph the basic cotangent function and adjust it based on these transformations, including marking intervals and plotting key points. The video concludes with a complete graph of the transformed function, emphasizing the importance of understanding the basic cotangent function to apply transformations effectively.

What is the function being transformed in this example?

• y = 2 * tan(1/4x)

• y = 2 * cot(1/4x)

• y = cot(2x)

• y = 1/4 * cot(2x)

How does the coefficient of x, known as variable B, affect the cotangent function?

• It changes the amplitude.

• It affects the period.

• It shifts the graph horizontally.

• It reflects the graph over the x-axis.

What is the period of the function y = 2 * cot(1/4x)?

• 8PI radians

• PI radians

• 2PI radians

• 4PI radians

What is the effect of the coefficient 2 in the function y = 2 * cot(1/4x)?

• It compresses the graph horizontally.

• It stretches the graph vertically by a factor of 2.

• It shifts the graph vertically.

• It reflects the graph over the y-axis.

What is the period of the basic cotangent function?

• PI radians

• 4PI radians

• 1/2PI radians

• 2PI radians

Where are the vertical asymptotes located for the basic cotangent function?

• At 0 and 2PI radians

• At PI/2 and 3PI/2 radians

• At 0 and PI radians

• At PI/4 and 3PI/4 radians

How is the interval from 0 to 4PI divided for graphing the transformed function?

• Into 2 equal parts

• Into 5 equal parts

• Into 3 equal parts

• Into 4 equal parts

What is the function value at the first quarter of the interval for the transformed function?

• 0

• 1

• 2

• -1

What is the function value at the third quarter of the interval for the transformed function?

• 0

• 1

• -1

• -2

What is the key to graphing transformations of the cotangent function?

• Memorizing the transformed function

• Using a calculator

• Knowing the key components of the basic cotangent function

• Ignoring the vertical asymptotes