Trigonometric Functions and Transformations

The video tutorial explains how to analyze and graph the function y = 3 * tangent(2x + π/2). It covers the concepts of period, vertical and horizontal shifts, and how to factor the function for graphing. The tutorial also demonstrates how to graph the transformed tangent function by identifying key points and vertical asymptotes, emphasizing the effect of the coefficient on vertical stretching.

What is the main task described in the introduction of the video?

• Identifying the function's domain

• Determining the period and horizontal shift

• Finding the amplitude of the function

• Calculating the vertical shift

Which trigonometric functions do not have an amplitude?

• All trigonometric functions

• Secant and Cosecant

• Tangent and Cotangent

• Sine and Cosine

How is the period of a tangent function calculated?

• π/B

• B/2π

• B/π

• 2π/B

What is the effect of a positive constant C on the graph of a function?

• Shifts the graph down

• Shifts the graph up

• Stretches the graph vertically

• Compresses the graph horizontally

What is the horizontal shift of the function after factoring?

• Left π/2 radians

• Right π/2 radians

• Right π/4 radians

• Left π/4 radians

What is the period of the function after factoring?

• π/2

• π/4

• π

• 2π

What happens to the tangent function when the coefficient is 3?

• It shifts horizontally

• It compresses vertically

• It stretches vertically

• It compresses horizontally

Where is the function value zero in the transformed graph?

• At the origin

• At -π/4 radians

• At π/4 radians

• At π/2 radians

How is the graph extended across multiple periods?

• By shifting the graph vertically

• By recalculating the period

• By changing the amplitude

• By copying and pasting the initial graph

What is the function value at 1/4 of the period to the right of the center?

• Positive 1

• Negative 1

• Positive 3

• Negative 3